Finite-Time H_∞ Control for Nonlinear Stochastic Systems via T-S Fuzzy models

This paper presents a comprehensive study on finite-time H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for nonlinear stochastic systems incorporating both Wiener and Poisson noise via T-S fuzzy models. Initially, leveraging the Itô-Levy formula and matrix inequality technique, we derive sufficient conditions for mean-square finite-time bounded (MSFTB). Following this, we design an observer-based fuzzy controller and formulate sufficient conditions that guarantee the existence of observer-based MSFTB H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controllers. Ultimately, we provide an illustrative example to demonstrate the validity of our proposed results.