Robust $\mathcal {H}_{\infty }$-Based Control for Uncertain Stochastic Fuzzy Switched Time-Delay Systems via Integral Sliding Mode Strategy

Abstract

In this article, we investigate the problems of robust exponential stabilization in mean square and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -based integral sliding mode controller design for uncertain stochastic Takagi–Sugeno (T-S) fuzzy switched time-delay systems with both matched and unmatched uncertainties under synchronous switching and asynchronous switching, respectively. In these systems, the control input is dependent on a switching signal. Under synchronous switching and asynchronous switching, sufficient conditions are developed to guarantee that the resulting closed-loop systems are robustly exponentially stable in mean square with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -performance, respectively. The integral sliding mode surfaces and the sliding mode controllers are designed for the underlying systems under synchronous switching and asynchronous switching, respectively. By two examples stemming from the mass–spring–damper model and the single-link robot arm model under stochastic perturbation, the effectiveness of the results obtained is verified.