Asynchronous H∞ control for uncertain singular stochastic Markov jump systems with multiplicative noise based on hidden Markov mode

Abstract

This paper is dedicated to the asynchronous H∞ output feedback control for a class of discrete-time uncertain singular stochastic Markov jump systems (SSMJSs) with multiplicative noise. The parametric uncertainties here are allowed to be norm-bounded. The asynchronous phenomenon between original modes and controller modes leads to the resultant closed-loop system constructing a hidden Markov model (HMM). A convinced and detailed proof for the first time is proposed to ensure nominal SSMJSs with multiplicative noise and completely known information to be stochastically admissible with a prescribed H∞ performance. To conquer the nonlinear difficulties incurred by the coupling of Lyapunov variables and controller gains, several effective strategies such as the matrix augmentation, special decomposition and introduction of auxiliary matrices are used. Furthermore, even in the simultaneous presence of singularity, multiplicative noise, parametric uncertainties as well as partial observation information, an asynchronous output feedback controller is successfully designed such that the uncertain SSMJS with multiplicative noise is stochastically admissible while achieving the required H∞ performance. Finally, numerical examples are presented to demonstrate the effectiveness of proposed results.