Linear Systems With Medium-Access Constraint and Markov Actuator Assignment

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.