Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems

This article investigates the reachable set synthesis problem for delay nonlinear hidden Markovian jump systems (NHMJSs) subject to asynchronous control strategy. The purpose is to find a suitable fuzzy controller to ensure that all the states of the generated closed-loop NHMJSs are bounded in the predetermined ellipsoidal region. First of all, Takagi–Sugeno (T–S) fuzzy model is used to approximate the nonlinear dynamics systems (NDS). On this basis, the hidden Markov model (HMM) is introduced to represent the asynchronous phenomenon among the controller modes and subsystem modes. Under taking time-varying delays into account, two descriptions of the reachable set ellipsoidal bound are provided. In addition, the relevant parameters of the fuzzy asynchronous controller are obtained by selecting the Lyapunov functionals with two different mode-dependent matrices, respectively. Finally, some numerical examples are given to verify the feasibility of the method proposed in this paper.