Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems

Abstract This paper concentrates on solving the finite-time bounded control problem for a family of discrete-time Takagi–Sugeno fuzzy Markov jump systems with a memory state feedback controller. In the proposed controller design, the non-fragile control protocol is considered to overcome the effect of gain perturbations and a more practical actuator fault model is employed to tolerate the time-varying faults. With the aid of a mode-dependent Lyapunov–Krasovskii functional and the Abel lemma-based finite sum inequality, sufficient conditions ensuring the stochastic finite-time boundedness for the closed-loop system are derived in the framework of matrix inequalities. Under which, a desired extended passivity performance index is guaranteed for the system under consideration. The proposed memory state feedback controller gains are computed by solving the derived matrix inequalities. Further, the feasibility and virtue of obtained theoretical findings are illustrated through two practical models, namely, single link robot arm system and Henon system.