Asynchronous H∞ Control for Continuous-Time Hidden Markov Jump Systems With Actuator Saturation.

Abstract

In this article, we address the asynchronous H∞ control problem of a class of hidden Markov jump systems (HMJSs) subject to actuator saturation in the continuous-time domain. A bunch of convex hulls is utilized to represent the saturated nonlinearity. Considering that there is an asynchronous mode mismatch between the system and the controller, we establish a hidden Markov model (HMM) to simulate the situation. By means of the Lyapunov theory, sufficient conditions are presented to ensure that the resultant closed-loop HMJS is stochastically mean square stable within the domain of attraction with a prescribed H∞ performance index. Furthermore, the state feedback gain matrix and the estimation of the domain of attraction are given by solving an optimization problem, which is constructed via linear matrix inequality (LMI) techniques. Finally, the reliability and validity of the derived results are examined by a numerical example.