Dynamic Output Feedback Finite-Time H∞ Control for Discrete-Time T-S Fuzzy Stochastic Uncertain Systems

Abstract

Using the T-S model, this article discusses the dynamic output feedback (DOF) finite-time $H$∞ control (FTHC) problem for a category of discrete-time stochastic systems (DTSSs) with time-varying norm bounded uncertain terms. Initially, the notion of finite-time $H$∞ boundedness is given. Then, by the method of Lyapunov functional, sufficient criteria are introduced for the obtaining closed-loop system (CLS) to be finite-time bounded and the influence of disturbing input on the controlled output to be restrained within a certain level. Furthermore, sufficient conditions on finite-time $H$∞ bounded (FTHB) for the CLS utilizing a DOF controller are presented, and the DOF control gain can be obtained by solving the optimization problem for linear matrix inequalities (LMIs). Finally, the validity of the proposed approach is illustrated by a simulation example.