Event-Based Multiagent Consensus Control: Zeno-Free Triggering via Lp Signals.

In this paper, we develop some new event-triggered algorithms for achieving distributed consensus for a multiagent system that guarantees fully Zeno-free triggerings for all the agents. In the proposed framework, each agent updates its control input only at its own triggering instants by using local measurements (i.e., relative states) with respect to neighboring agents, and such local measurements can be done in a local coordinate frame. For all agents, a positive Lp signal function is embedded in the event detector functions, which aims to avoid the possible comparison of an event error term to a zero threshold that may happen in a zero-crossing scenario. We further propose a Zeno-free self-triggered algorithm to achieve multiagent consensus, which enables discrete-time measurements and thus avoids continuous measurements between the neighboring agents. We also show that the proposed event-based consensus algorithms guarantee less frequent triggered events in a bounded time interval compared to the conventional algorithm without Lp signals. Simulations and comparisons are provided to validate the performance and effectiveness of the proposed event-based consensus schemes.

Growing Super Stable Tensegrity Frameworks.

This paper discusses methods for growing tensegrity frameworks akin to what are now known as Henneberg constructions (HCs), which apply to bar-joint frameworks. In particular, this paper presents tensegrity framework versions of the three key HCs of vertex addition, edge splitting, and framework merging (where separate frameworks are combined into a larger framework). This is done for super stable tensegrity frameworks in an ambient 2-D or 3-D space. We start with the operation of adding a new vertex to an original super stable tensegrity framework, named vertex addition. We prove that the new tensegrity framework can be super stable as well if the new vertex is attached to the original framework by an appropriate number of members, which include struts or cables, with suitably assigned stresses. Edge splitting can be secured in [Formula: see text] ( [Formula: see text]) by adding a vertex joined to three (four) existing vertices, two of which are connected by a member, and then removing that member. This procedure, with appropriate selection of struts or cables, preserves super-stability. In d -dimensional ambient space, merging two super stable frameworks sharing at least d +1 vertices that are in general positions, we show that the resulting tensegrity framework is still super stable. Based on these results, we further investigate the strategies of merging two super stable tensegrity frameworks in IRd , ( d ∈ {2,3} ) that share fewer than d +1 vertices, and show how they may be merged through the insertion of struts or cables as appropriate between the two structures, with a super stable structure resulting from the merge.

On the Sensitivity of Granger Causality to Errors-In-Variables, Linear Transformations and Subsampling.

This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger-causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors-in-variables case, we give a continuity result, which implies that: a 'small' noise-to-signal ratio entails 'small' distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which 'spurious' causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches.

Autoregressive models of singular spectral matrices.

This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description [Formula: see text] with [Formula: see text] a tall constant matrix of full column rank and with the determinantal zeros of [Formula: see text] all stable, i.e. in [Formula: see text]. To obtain a parsimonious AR model, a canonical form is derived and a number of advantageous properties are demonstrated. First, the maximum lag of the canonical AR model is shown to be minimal in the equivalence class of AR models of the same transfer function matrix. Second, the canonical form model is shown to display a nesting property under natural conditions. Finally, an upper bound is provided for the total number of real parameters in the obtained canonical AR model, which demonstrates that the total number of real parameters grows linearly with the number of rows in [Formula: see text].

Properties of blocked linear systems.

This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature.