Resilient Asynchronous H∞ Control for Discrete-Time Markov Jump Singularly Perturbed Systems Based on Hidden Markov Model

Abstract

This paper studies the resilient asynchronous H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem for slow sampling discrete-time uncertain Markov jump singularly perturbed systems (SPSs). Compared with slow state variables feedback controller, a new controller is proposed for slow sampling discrete-time SPSs, which has less conservatism. A more realistic situation, i.e., the system modes cannot be directly acquired for controller design, is considered with the help of hidden Markov model (HMM). The goal is to design a resilient asynchronous controller based on HMM such that the closed-loop system is stochastically stable while meeting an expected H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance in the presence of random controller gain fluctuation and the system modes hiding for controller. By utilizing matrix inequality techniques and Lyapunov function method, some criteria are established for the existence of the resilient asynchronous controller. The superiority and practicability of the obtained theoretical results are demonstrated by a numerical example and an inverted pendulum system.