Hidden Markov model based finite-time H∞ guaranteed cost control for singular discrete-time Markov jump delay systems

Abstract

Considering partially known transition rates and saturating actuators, the finite-time H∞ control problem for a class of singular discrete-time Markovian jump delayed systems is studied in this article. First, by employing local sector conditions and an appropriate Lyapunov function, a hidden Markov model based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally finite-time stabilizable, and the closed-loop cost function value is not more than a specified upper bound. Furthermore, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.