Dissipative Constraint-Based Saturation Control for Fuzzy Markov Jump Systems Within a Finite-Time Interval

This paper deals with the problems of finite-time boundedness and dissipative analysis for a class of discrete-time nonlinear Markov jump systems (MJSs) with disturbances. In particular, the Takagi-Sugeno fuzzy model is applied to the nonlinear plant, and the impact of time-varying actuator saturation is considered in the controller design. The main purpose of this paper is to develop a mode-dependent fuzzy saturation control for fuzzy MJSs over a finite-time interval. With the help of the Lyapunov stability theory and Abel lemma-based finite-sum inequality, it is established that convergence of all states are confirmed through the addressed control design. Correspondingly, the resulting closed-loop system is stochastically finite-time bounded and \(({\mathcal {Q}},{\mathcal {S}},{\mathcal {R}})\) $(\mathcal{Q},\mathcal{S},\mathcal{R})$ - \(\gamma\) $\gamma$ -dissipative under linear matrix inequality (LMI) framework. At last, two numerical examples are given to demonstrate the effectiveness and usefulness of the obtained LMI conditions.