Resilient estimation for T-S fuzzy descriptor systems with semi-Markov jumps and time-varying delay

Abstract This paper concerns the resilient estimation problem for nonlinear descriptor semi-Markov jumps systems (S-MJSs) with time-varying delay via Takagi–Sugeno (T-S) fuzzy model, where descriptor S-MJSs, T-S fuzzy model and resilient estimator design are firstly considered in a unified framework. The estimator to be designed is assumed to have additive gain perturbations. First, by constructing a comprehensive stochastic Lyapunov–Krasovskii functional, a sufficient condition is given such that the estimation error systems are stochastically admissible and have a prescribed H∞ noise attenuation performance index. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented, which guarantees the estimation error systems are stochastically admissible and achieve a prescribed H∞ noise attenuation performance index. Meanwhile, the resilient fuzzy estimator is developed, which can be of full-order or reduced-order. The proposed design method doesn’t impose any constraints on slack variables, which are less conservative. Last, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.