Finite-Time H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers.

This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches.

Asynchronous fault detection filtering for Markovian jump systems with output sensor saturation.

In this paper, a robust asynchronous filter is proposed to detect faults in Markovian jump systems with sensor saturations. The proposed filter has a mode different from that of the original system, and is tolerant of external disturbances. The residual is generated to construct an evaluation function that can successfully perform fault detection. Detailed filter matrices can be computed from the existing conditions. Furthermore, practical and comparative simulations are performed to verify the efficiency of the proposed technique.

Decentralized Finite-time L2-L∞ tracking control for a class of interconnected Markovian jump system with actuator saturation.

An observer-based decentralized tracking control technique is developed for a saturated interconnected Markovian jump system in the sense of finite-time stability (FTS). To improve tracking performances, a L2-L∞ performance criterion which is relevant to both estimated error and estimated tracking error is proposed. A sufficient condition for finite-time bounded (FTB) is established. In view of the obtained condition, a method with the one-step procedure to seek the gains of observer and controller is investigated. By virtue of this procedure, the problem of the decentralized tracking stabilization is transformed into a convex optimization problem subject to constraints in the form of linear matrix inequalities (LMIs). Furthermore, the tracking control problem of interconnected Markovian jump system without saturation is also investigated, and the results are obtained directly to avoid taking congruent transformation. Simulation is presented to show the effectiveness and applicability of the obtained results.

Nonfragile H∞ control for periodic stochastic systems with probabilistic measurement.

This paper addresses the problem of nonfragile H∞ control for periodic stochastic systems with probabilistic measurement. A novel Lyapunov-Krasovskii functional is formulated, which makes full use of both delay and its change rate. In view of the measurement signal, the mode-dependent stochastic variables are employed and new sufficient conditions are achieved. Finally, two numerical examples are worked out to demonstrate the effectiveness of the proposed control design.

H∞ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties.

This paper deals with the problem of robust H∞ fault detection for a class of stochastic Markovian jump systems (SMJSs) The aim is to design a linear mode-dependent fault detection filter such that the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. By using Lyapunov stability theory and generalized Itô formula, some novel mode-dependent and delay-dependent sufficient conditions in terms of linear matrix inequality (LMI) are proposed to insure the existence of the desired fault detection filter. A simulation example and an industrial nonisothermal continuous stirred tank reactor (CSTR) system are employed to show the effectiveness of the proposed method.

Finite-time boundedness filtering for discrete-time Markovian jump system subject to partly unknown transition probabilities.

This paper investigates the problem of finite-time boundedness filtering for discrete-time Markovian jump system subject partly unknown transition probabilities. By using the multiple Lyapunov function approach, a novel sufficient condition for finite-time bounded of H∞ filtering is derived and the system trajectory stays within a prescribed bound during a specified time interval. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.