Co-design of non-fragile observer and controller for T-S fuzzy semi-Markov systems under time delay and actuator faults

This paper proposes a unified co-design architecture for a non-fragile observer and controller for Takagi-Sugeno (T-S) fuzzy semi-Markov jump systems (SMJS) subject to time delays, actuator faults, and parameter uncertainties. A comprehensive system model is first established that integrates T-S fuzzy rules with semi-Markov chains (SMC) to capture both nonlinear dynamics and stochastic switching with dwell-time-dependent transitions. To estimate the unmeasurable system states and hidden operational modes, a mode-detection observer is constructed. Concurrently, a non-fragile output-feedback controller is co-designed to robustly compensate for actuator failures and inherent gain fluctuations in the control unit itself. By constructing a novel augmented stochastic Lyapunov-Krasovskii functional(LKF) that fully incorporates the time delay, sufficient conditions in the form of linear matrix inequalities (LMIs) are derived to guarantee robust exponential mean-square stability on the closed-loop system in fault-prone environments. Consequently, the proposed approach offers a verifiable and tractable solution, as validated by comparative simulations.