Proportional integral observer-based input–output finite-time stabilization for chaotic semi-Markov jump fuzzy systems

The goal of this article is to discuss the input–output finite-time (IO-FT) stabilization and state estimation problem for T-S fuzzy chaotic semi-Markov jump systems (TSFCS-MJSs) with uncertain transition rates, immeasurable states, quantization errors, gain fluctuations and external input signals by using quantized resilient proportional integral (PI) observer-based control. Precisely, to estimate the immeasurable states of the underlying TSFCS-MJSs, a mode-dependent fuzzy rule-based PI observer is implemented, wherein the inclusion of both proportional and integral loops provides more design freedom and finer steady-state accuracy. Additionally, the gain fluctuations that occur during the implementation of the addressed PI observer are taken into account and therefore, we focus on the design of resilient PI observer that provides satisfactory estimation results. Besides, by reason of the restricted capacity of the data transmission medium, the input signals are quantized prior to transmission. Following that, sufficient criteria are attained in the framework of linear matrix inequalities with the use of a mode-dependent Lyapunov function candidate can guarantee the resulting closed-loop system’s IO-FT stability. Thereafter, by solving the established linear matrix inequality-based criteria, the desired gain matrices of the controller and observer are computed. Finally, the simulation outcomes for standard Chua’s circuit system are displayed in accordance with the theoretical findings.