Robust resilient controller design for uncertain discrete-time fuzzy Markovian jump delayed systems

This paper investigates the problem of robust stabilization for a class of nonlinear discrete-time Markovian jump delayed systems using the Takagi-Sugeno (T-S) fuzzy model approach. The time delays are assumed to be time-varying and related to the mode, especially their bounds are also mode-dependent. Our aim is to design a resilient fuzzy Markovian switched controller such that the resulting closed-loop system is robustly stochastically stable. Based on an improved Markovian switched fuzzy-basis-dependent Lyapunov functional, some delay-dependent conditions for the solvability of this problem are derived in terms of relaxed linear matrix inequalities (LMIs), the desired resilient fuzzy controller can be designed through solving these LMIs. A numerical example is provided to illustrate the effectiveness of the proposed approach.