Linear systems with medium-access constraint and Markov actuator assignment

Authors:
Ge Guo
Affiliations:
School of Information Sciences and Technology, Dalian Maritime University, Dalian, China
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

This paper investigates a type of systems controlled over a communication network that can only accommodate a subset of actuators at any time. The medium-access status of actuators is event driven by a stochastic process modeled as a Markov chain. A methodology of analysis and control synthesis is established using theories in time-delay systems and Markovian jumping systems. Specifically, in the context of asymptotic mean-square stability, a state feedback control approach is derived by transforming the vector system into a scalar representation first and then using on it a stability criterion provided for scalar linear time-delay systems. The results are given in terms of a delay-dependent scalar inequality and a simple matrix inequality based on a couple of scalar decision variables, which are easily solvable using the newly proposed quasi-convex optimization algorithm. The corresponding results for uncertain linear systems are also given. Meanwhile, a design approach in the sense of stochastic stability in probability is presented using a Lyapunov-like method, with the mode-dependent results being given in the form of a set of coupled matrix differential inequalities and a martingale probability inequality. Numerical examples have shown the usefulness of the proposed results.