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1.
Brain Res Bull ; 217: 111064, 2024 Oct 15.
Article in English | MEDLINE | ID: mdl-39232993

ABSTRACT

OBJECTIVE: The diversity of electrode placement systems brought the problem of channel location harmonization in large-scale electroencephalography (EEG) applications to the forefront. Therefore, our goal was to resolve this problem by introducing and assessing the reference electrode standardization technique (REST) to transform EEGs into a common electrode distribution with computational zero reference at infinity offline. METHODS: Simulation and eye-closed resting-state EEG datasets were used to investigate the performance of REST for EEG signals and power configurations. RESULTS: REST produced small errors (the root mean square error (RMSE): 0.2936-0.4583; absolute errors: 0.2343-0.3657) and high correlations (>0.9) between the estimated signals and true ones. The comparison of configuration similarities in power among various electrode distributions revealed that REST induced infinity reference could maintain a perfect performance similar (>0.9) to that of true one. CONCLUSION: These results demonstrated that REST transformation could be adopted to resolve the channel location harmonization problem in large-scale EEG applications.


Subject(s)
Electrodes , Electroencephalography , Scalp , Humans , Electroencephalography/methods , Scalp/physiology , Rest/physiology , Brain/physiology , Signal Processing, Computer-Assisted , Brain Mapping/methods
2.
Front Robot AI ; 11: 1333837, 2024.
Article in English | MEDLINE | ID: mdl-39157793

ABSTRACT

This article introduces a model-based robust control framework for electrohydraulic soft robots. The methods presented herein exploit linear system control theory as it applies to a nonlinear soft robotic system. We employ dynamic mode decomposition with control (DMDc) to create appropriate linear models from real-world measurements. We build on the theory by developing linear models in various operational regions of the system to result in a collection of linear plants used in uncertainty analysis. To complement the uncertainty analyses, we utilize H ∞ ("H Infinity") synthesis techniques to determine an optimal controller to meet performance requirements for the nominal plant. Following this methodology, we demonstrate robust control over a multi-input multi-output (MIMO) hydraulically amplified self-healing electrostatic (HASEL)-actuated system. The simplifications in the proposed framework help address the inherent uncertainties and complexities of compliant robots, providing a flexible approach for real-time control of soft robotic systems in real-world applications.

3.
Cureus ; 16(5): e60936, 2024 May.
Article in English | MEDLINE | ID: mdl-38910766

ABSTRACT

Background The management of distal clavicle injuries with disruption of the coracoclavicular ligaments (CCLs) is challenging. The aim of this study was to assess the functional results of reconstructing the CCLs with the Infinity-Lock Button System using validated outcome measures, patient satisfaction scores, return to pre-injury activity, and complications. Methods A total of 28 cases of CCL disruption were assessed over a seven-year period, which included 14 lateral end-of-clavicle fractures and 14 acromioclavicular joint (ACJ) dislocations. All patients underwent stabilisation of the CCLs using the Infinity-Lock Button System. Patients were assessed preoperatively and postoperatively using validated outcome measures such as visual analogue scale (VAS), Oxford Shoulder Score (OSS), Quick Disabilities of Arm, Shoulder & Hand (Q-DASH) scores, return to pre-injury level of activities, patient satisfaction scores, and complications were reviewed. Results The mean age of patients was 36.7 years (18-74 years). The mean follow-up was 38.6 months (8-68 months). The mean time to surgery was 75.8 days (3-619 days). There was a statistically significant improvement in postoperative VAS, OSS, and Q-DASH scores compared to the preoperative (p-value <0.001). Out of the 28 participants, 23 (82.1%) returned to pre-injury level of activities, 25 (89.7%) reported 'good' or 'excellent' outcomes following the intervention, and none of the patients reported functional instability postoperatively. None of the patients required revision surgery or implant removal. Conclusion CCL reconstruction is vital in the management of clavicular injuries. This study demonstrates the safe use of the Infinity-Lock Button System in these injuries with statistically significant improvement in early patient-reported outcome measures, return to pre-injury level of activities, and subjective patient satisfaction.

4.
Trends Cell Biol ; 34(7): 527-530, 2024 Jul.
Article in English | MEDLINE | ID: mdl-38834379

ABSTRACT

This report aims to propose the novel term 'neutrophil endoplasmic reticulum (ER) stress' (NERS). NERS explores the influence of neutrophil extracellular trap (NET) formation and exacerbation of respiratory ailments. This inquiry aims to advance comprehension in neutrophil biology and respiratory health.


Subject(s)
Endoplasmic Reticulum Stress , Extracellular Traps , Inflammation , Neutrophils , Animals , Humans , Extracellular Traps/metabolism , Inflammation/pathology , Inflammation/metabolism , Neutrophils/metabolism
5.
Immunity ; 57(7): 1549-1566.e8, 2024 Jul 09.
Article in English | MEDLINE | ID: mdl-38776917

ABSTRACT

The activities, ontogeny, and mechanisms of lineage expansion of eosinophils are less well resolved than those of other immune cells, despite the use of biological therapies targeting the eosinophilia-promoting cytokine interleukin (IL)-5 or its receptor, IL-5Rα. We combined single-cell proteomics and transcriptomics and generated transgenic IL-5Rα reporter mice to revisit eosinophilopoiesis. We reconciled human and murine eosinophilopoiesis and provided extensive cell-surface immunophenotyping and transcriptomes at different stages along the continuum of eosinophil maturation. We used these resources to show that IL-5 promoted eosinophil-lineage expansion via transit amplification, while its deletion or neutralization did not compromise eosinophil maturation. Informed from our resources, we also showed that interferon response factor-8, considered an essential promoter of myelopoiesis, was not intrinsically required for eosinophilopoiesis. This work hence provides resources, methods, and insights for understanding eosinophil ontogeny, the effects of current precision therapeutics, and the regulation of eosinophil development and numbers in health and disease.


Subject(s)
Cell Lineage , Eosinophils , Interleukin-5 , Mice, Transgenic , Proteomics , Single-Cell Analysis , Transcriptome , Eosinophils/immunology , Eosinophils/metabolism , Animals , Interleukin-5/metabolism , Interleukin-5/genetics , Humans , Mice , Proteomics/methods , Single-Cell Analysis/methods , Cell Differentiation/immunology , Mice, Inbred C57BL , Gene Expression Profiling/methods , Interleukin-5 Receptor alpha Subunit/metabolism , Interleukin-5 Receptor alpha Subunit/genetics , Myelopoiesis/genetics , Interferon Regulatory Factors/metabolism , Interferon Regulatory Factors/genetics , Mice, Knockout
6.
J Contemp Dent Pract ; 25(1): 3-9, 2024 Jan 01.
Article in English | MEDLINE | ID: mdl-38514424

ABSTRACT

AIM: This study aimed to evaluate the marginal microleakage and maximum occlusal fracture loads and fracture modes of two novel class II preparation designs, "infinity edge" and the "2.5 mm cusp reduction" preparations as compared to a traditional class II preparation without cuspal involvement. MATERIALS AND METHODS: Thirty extracted human mandibular molars were prepared for moderate-sized class II restorations with extensions into all occlusal grooves. Of these, ten class II preparations served as control. Ten were modified for a 2.5 mm even reduction of the cusps adjacent to the interproximal box. An additional 10 preparations were modified with an "infinity edge" bevel on the interproximal and occlusal portions. All teeth were restored utilizing a flowable bulk-fill composite in the apical portion of the interproximal box and 2-4 mm of heated bulk-fill composite in one increment for the remainder. All groups were cyclic loaded and thermocycled, then imaged with microcomputed tomography (µCT) before and after infiltration with a silver nitrate solution. Images were subtracted to obtain volumetric measurements of microleakage and reported as a percentage of the total volume from the apical extent of the proximal box. All groups were loaded to failure and fracture load and mode were recorded. RESULTS: No significant differences were found in microleakage volume as a percentage of total tooth volume; however, the "infinity edge" group had significantly greater microleakage in the proximal box compared to the traditional class II group. No significant differences were found in fracture load or mode between the groups. CONCLUSION: Traditional class II, 2.5 mm cuspal reduction, and "infinity edge" preparation designs have similar fracture loads as well as volumes of microleakage; however, an "infinity edge" preparation has a higher ratio of microleakage in the proximal box. CLINICAL SIGNIFICANCE: Clinicians should carefully consider the use of "infinity edge" margins, particularly on dentin in the apical extent of the proximal box. How to cite this article: Watson JC, Lien W, Raimondi JC, et al. In Vitro Microleakage and Fracture Resistance of "Infinity Edge" and Cusp Reduction Preparation Designs for Moderate-sized Class II Composites. J Contemp Dent Pract 2024;25(1):3-9.


Subject(s)
Dental Leakage , Dental Restoration, Permanent , Humans , Dental Restoration, Permanent/methods , X-Ray Microtomography , Dental Cavity Preparation/methods , Dental Leakage/prevention & control , Composite Resins , Molar
7.
IBRO Neurosci Rep ; 16: 309-316, 2024 Jun.
Article in English | MEDLINE | ID: mdl-38390233

ABSTRACT

This study seeks to explore the correlation between cortical activation and the Infinity Walk pattern, examining how the influence of foot overpronation and footwear may impact motor control. Functional near-infrared spectroscopy (fNIRS), a portable and user-friendly neuroimaging technique, was used to measure hemodynamical changes in six individuals with non-critical pronation degrees. Participants perform the Infinity Walk under various footwear conditions while wearing an fNIRS portable imaging device. Results indicate a consistent hemodynamic pattern in both hemispheres during the Infinity Walk, with no significant differences observed across subjects and footwear conditions in the prefrontal cortex (PFC), pre-motor area, the supplementary motor cortex (PMA & SMC), the primary motor cortex (PMC), and Wernicke's area (WA). The impact of pronation and footwear on motor control remains inconclusive due to inconsistent hemodynamic patterns. Notably, the activation patterns in Broca's area (BA) and the temporal gyrus (TG) differ significantly from other brain regions. The balanced hemodynamic responses in the bilateral hemispheres may be attributed to the Infinity Walk's inherent walking pattern. These findings indicate a need for further investigation into the Infinity Walk to examine the similarities and distinctions in activation patterns within specific brain regions. Additionally, the impact of pronation necessitates more substantial experimental research to establish a correlation between pronation and cortical hemodynamics.

8.
J Relig Health ; 63(2): 1642-1660, 2024 Apr.
Article in English | MEDLINE | ID: mdl-38253751

ABSTRACT

Apeiroanxiety is a fear of infinity. Some people may experience anxiety or discomfort when contemplating the vastness or endless nature of certain concepts, such as time or space. Addressing any form of anxiety is important as it can impact an individual's daily functioning, wellbeing, and quality of life. The current study is aimed at developing a reliable and valid measure of apeiroanxiety in the context of the afterlife for the Pakistani Muslim population. The research had three studies: Query Study I generated an item pool of 18 items based on a literature review, semi-structured interviews, and expert opinion. This item pool was administered to a convenient sample of Pakistani Muslim participants (n = 1277). As a result of exploratory factor analysis, a uni-dimensional factor solution with five items was yielded (α = 0.90). Confirmatory factor analysis confirmed the obtained uni-dimensional factor solution in study II of the research with an excellent model fit. In study III, the convergent and discriminant validity of the scale was established on a separate independent sample (n = 485). Results yielded evidence of convergent validity as negative afterlife belief and rumination had a positive correlation with apeiroanxiety. The discriminant validity was established by a non-significant relationship between positive afterlife belief and apeiroanxiety. Moreover, the limitations, suggestions, and implications of the study are discussed.


Subject(s)
Islam , Quality of Life , Adult , Humans , Surveys and Questionnaires , Pakistan , Psychometrics/methods , Reproducibility of Results
9.
Philos Trans A Math Phys Eng Sci ; 382(2267): 20230035, 2024 Mar 04.
Article in English | MEDLINE | ID: mdl-38219780

ABSTRACT

This paper is about two important trends of scattering theory in general relativity: time-dependent spectral analytic scattering and conformal scattering. The former was initiated by Jonathan Dimock and Bernard Kay in the mid-1980s and is based on spectral and functional analysis. The latter was proposed by Roger Penrose in 1965 and then constructed for the first time by Gerard Friedlander in 1980 by putting together Penrose's conformal method and another analytic approach to scattering: the Lax-Phillips theory due to Peter Lax and Ralph Phillips. We shall review the history of the two approaches and explain their general principles. We shall also explore an important question: 'can the tools of one approach be used to obtain a complete construction in the other?' This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

10.
Philos Trans A Math Phys Eng Sci ; 382(2267): 20230045, 2024 Mar 04.
Article in English | MEDLINE | ID: mdl-38219778

ABSTRACT

The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski space-time is studied by means of Friedrich's cylinder at spatial infinity. The results are applied to a system of equations called the good-bad-ugly which serves as a model for the Einstein field equations in generalized harmonic gauge. The relation between the logarithmic terms (polyhomogeneity) appearing in the solution obtained using conformal methods and those obtained by means of a heuristic method based on Hörmander's asymptotic system is discussed. This review article is based on Duarte et al. (Duarte et al. 2023 Class. Quantum Gravity 40, 055002. (doi:10.1088/1361-6382/acb47e)); Gasperín & Pinto (Gasperín & Pinto 2023 Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime. J. Math. Phys. 64, 082502. (doi:10.1063/5.0158746)). This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

11.
Article in English | MEDLINE | ID: mdl-38164100

ABSTRACT

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instant around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.

12.
Philos Trans A Math Phys Eng Sci ; 382(2267): 20230041, 2024 Mar 04.
Article in English | MEDLINE | ID: mdl-38219775

ABSTRACT

This paper describes conservation laws in general relativity (GR) dating back to the mass-energy conservation of Bondi and Sachs in the early 1960s but using 2-spinor techniques. The notion of conformal infinity is employed, and the highly original ideas of E. T. Newman are discussed in relation to twistor theory. The controversial NP constants are introduced, and their meaning is considered in a new light related to the problem of equations of motion in GR. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

13.
Philos Trans A Math Phys Eng Sci ; 382(2267): 20230048, 2024 Mar 04.
Article in English | MEDLINE | ID: mdl-38219787

ABSTRACT

This is an introductory article for the proceedings associated with the Royal Society Hooke discussion meeting of the same title which took place in London in May 2023. We review the history of Penrose's conformal compactification, null infinity and a number of related fundamental developments in mathematical general relativity from the last 60 years. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

14.
China Medical Equipment ; (12): 19-23, 2024.
Article in Chinese | WPRIM (Western Pacific) | ID: wpr-1026517

ABSTRACT

Objective:To investigate the effects of different tube voltages combined with artificial intelligence reconstruction algorithm(CI)on the computed tomography(CT)imaging quality and radiation dose of chest phantom on the basis of the CT scan for an adult male simulated chest phantom(PH-N1).Methods:A 512-slice CT scanner of ultrahigh-end was adopted to conduct scan,and the images were divided into 70 kV group,80 kV group,100 kV group and 120 kV group according to different tube voltage.For 4 groups of CT scan images with different tube voltages,the 10%,30%,50%,70%and 90%CI were adopted to reconstruct 1mm thin layer image.The CT volume dose index(CTDIvol)and the dose-length product(DLP)of the scans of 4 groups were compared.The CT values and standard deviation(SD)values of the aorta,abdominal wall fat and erector spine muscle were measured.Two senior diagnostic physicians with more than 5 years of work experience independently and double-blindly evaluated the image quality by using 5-point scale.A Kappa consistency test was conducted.One-way analysis of variance was adopted to compare the differences of CT values and SD values of the tissues of image targets.The Friedman rank-sum test was adopted to compare the differences of subjective image qualities among different groups.Results:The differences of CTDIvol and DLP among 4 groups with different tube voltages were significant(F=1855.617,3996.118,P<0.05),respectively.Under 70 kV tube voltage,there were no significant differences in CT values of the aorta,abdominal wall fat and erector spine muscle,which were reconstructed by using 10%,30%,50%,70%and 90%CI(P>0.05),while the differences of SD values among them were statistically significant(F=32.267,53.327,14.873,P<0.05),respectively.Under the different tube voltages of 4 groups,which were reconstructed by 90%CI,the CT values of aorta,abdominal wall fat and erector spine muscle gradually decreased with decreasing of tube voltage,the differences were significant(F=139.899,2563.93,219.231,P<0.05),respectively.The consistency of subjective scores between two diagnostic physicians was better for each group of images(Kappa=0.712~0.869).Conclusion:Compared with 80 kV,90 kV and 120 kV images,the reconstructed images with 90%CI algorithm under 70 kV tube voltage can significantly reduce the radiation dose,and the images have a favorable signal-to-noise ratio at the same time.

15.
Heliyon ; 9(12): e22825, 2023 Dec.
Article in English | MEDLINE | ID: mdl-38125542

ABSTRACT

In this paper, the Gaussian optical properties and the first- and third-order isotropic and anisotropic chromatic aberrations of the Glaser magnetic lens have been derived analytically and then calculated numerically based on two methods: the differential-algebraic DA and the electron optical aberration integrals. These coefficients have been recalculated for object magnetic immersion OMI. The expressions of chromatic aberration coefficients with the inclusion of the OMI effect of round electron lenses were not published in the literature until the present work. The numerical results of high-order chromatic aberration coefficients of Glaser magnetic lenses calculated using the DA method are shown to be in excellent agreement with those calculated using the integral aberration method and with the minor relative errors of order (10-7- 10-8), indicating that all the formulas for the chromatic aberration coefficients are entirely correct. For this purpose, COSY INFINITY 10 and Mathematica 11 were used, and both proved to be excellent computer programs for this work.

16.
Foot Ankle Int ; 44(12): 1247-1255, 2023 12.
Article in English | MEDLINE | ID: mdl-37964445

ABSTRACT

BACKGROUND: The Infinity Total Ankle Arthroplasty (Stryker, Mahwah, NJ) is a low-profile fixed-bearing implant first introduced in 2014. Although the short-term survivorship (2-4 years follow-up) and complication rates of the Infinity TAA have been reported, there are limited midterm outcome reports. The aim of this study was to describe the survivorship and clinical outcomes of a single-center experience with the Infinity implant at minimum 5-year follow-up. METHODS: Retrospective review of 65 ankles that underwent primary total ankle arthroplasty (TAA) with the Infinity implant was conducted. Mean clinical follow-up was 6.5 years (range, 5.0-8.0). Preoperative and postoperative radiographs were measured to assess tibiotalar alignment, periprosthetic lucencies, and cysts. Preoperative, 2-year, and 5-year postoperative Foot and Ankle Outcome Score (FAOS) subscores were compared to assess midterm clinical outcomes. Survivorship assessment was determined by removal of 1 or both metallic implant components. RESULTS: Survivorship of the implant was 93.8% at final follow-up. There were 4 revisions: 2 for tibial implant loosening, 1 for talar loosening, and 1 for loosening of both components. Three of the 4 revisions occurred within the first 2 years following implantation, and the last failure occurred at 7 years postoperatively. There were 11 reoperations in 10 (15%) ankles and 3 wound complications. There were 17 ankles (26.2%) with radiographic abnormalities around the implants, including 14 cases with tibial component lucencies and 4 cases of periimplant cysts. FAOS outcome measurement showed general stability between 2 and 5 years and substantial improvement from preoperative status. CONCLUSION: To date this study is the largest midterm report on the Infinity total ankle prosthesis, with 65 implants at a mean follow-up of 6.5 years. We found good midterm implant survivorship, and patients experienced significant improvements in FAOS outcome scores and radiographic alignment at final follow-up. LEVEL OF EVIDENCE: Level III, retrospective cohort study.


Subject(s)
Arthroplasty, Replacement, Ankle , Cysts , Joint Prosthesis , Humans , Ankle/surgery , Retrospective Studies , Survivorship , Prosthesis Failure , Prosthesis Design , Ankle Joint/diagnostic imaging , Ankle Joint/surgery , Reoperation , Treatment Outcome
17.
Sensors (Basel) ; 23(22)2023 Nov 10.
Article in English | MEDLINE | ID: mdl-38005480

ABSTRACT

A valve-controlled hydraulic motor system operating in a complex environment is subject to complex load changes. In extreme cases, the load can be regarded as a disturbance signal with complex frequency and strong amplitude fluctuations, which greatly affects the speed stability of the hydraulic motor and reduces the operating efficiency. In this paper, the structure of valve-controlled hydraulic motor systems is analyzed, and a valve-controlled hydraulic motor system model with uncertain parameters is established after considering the actual target parameter error and model linearization error. Different from the common H-infinity control, which regards the load disturbance as external disturbance, this paper presents a robust H-infinity tracking control strategy, which considers uncertain parameters and the load torque of the valve-controlled hydraulic motor system as internal disturbances. The simulation results show that the proposed control scheme has better control characteristics and robustness than the traditional PID control.

18.
Synthese ; 202(3): 81, 2023.
Article in English | MEDLINE | ID: mdl-37655125

ABSTRACT

Philosophers of mathematics often rely on the historical progress of mathematics in support of mathematical realism. These histories typically build on formal semantic tools to evaluate the changes in mathematics, and on these bases present later mathematical concepts as refined versions of earlier concepts which are taken to be vague. Claiming that this view does not apply to mathematical concepts in general, we present a case-study concerning projective geometry, for which we apply the tools of cognitive linguistics to analyse the developmental trajectory of the domain. On the basis of this analysis, we argue for the existence of two conceptually incompatible inferential structures, occurring at distinct moments in history, both of which yield the same projective geometric theorems; the first invoked by the French mathematicians Girard Desargues (1591-1661) and Jean-Victor Poncelet (1788-1867), and the second characterising a specific modern mode. We demonstrate that neither of these inferential structures can be considered as a refinement of the other. This case of conceptual development presents an issue to the standard account of progress and its bearing on mathematical realism. Our analysis suggests that the features that distinguish the underlying conceptually incompatible inferential structures are invisible to the standard application of the tools of formal semantics. Thus this case-study stands as an example of the manner and necessity of linguistics-specifically cognitive linguistics-to inform the philosophy of mathematics.

19.
Stud Hist Philos Sci ; 101: 48-60, 2023 10.
Article in English | MEDLINE | ID: mdl-37690232

ABSTRACT

Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.


Subject(s)
Cultural Diversity , Insufflation , Probability , Probability Theory
20.
Heliyon ; 9(8): e18924, 2023 Aug.
Article in English | MEDLINE | ID: mdl-37600380

ABSTRACT

This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of the second-order plant with three uncertain parameters. The applied graphical method, adopted from the authors' previous work, is grounded in finding the contour that is linked to the pairs of P-I coefficients marginally fulfilling the condition of robust relative stability expressed using the H∞ norm. The illustrative example in the current article emphasizes that the technique itself for plotting the boundary contour of robust relative stability needs to be combined with the precondition of the nominally stable feedback control system and with the line for which the integral parameter equals zero in order to get the final robust relative stability regions. The calculations of the robust relative stability regions for various robust stability margins α are followed by the demonstration of the control behavior for two selected controllers applied to a set of members from the family of plants.

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