Abstract

This paper investigates an asynchronous H_∞ control strategy for a class of discrete-time Markovian jump linear system (MJLS) subject to hard time domain constraints. The word “asynchronous” means that the switching of candidate controllers has a lag to the jump of system modes. First, new results on the mean square stability and H_∞ performance analysis for MJLS are given with average dwell time (ADT) bound by allowing the stochastic Lyapunov-like function (LLF) to increase during the running time of each active mode. The internal relationship between ADT and transition probabilities (TPs) is revealed by fully making use of the jump knowledge. Then, the asynchronous H_∞ controller for MJLS subject to input/output constraints is designed with the aid of a set of stochastic invariant ellipsoids. Moreover, the domain of the admissible set is enlarged by constructing a set of polyhedral invariant sets on-line with the designed controller. Finally, numerical examples are given to verify the potential of the developed results.

Keywords: Average dwell time, Asynchronous control, Markovian jump linear system, Polyhedron invariant set.