Notice of Removal: Sliding Mode Control of Fuzzy Singularly Perturbed Systems with Application to Electric Circuit

This paper presents a new sliding mode control (SMC) design methodology for fuzzy singularly perturbed systems (SPSs) subject to matched/unmatched uncertainties. To fully accommodate the model characteristics of the systems, a novel integral-type fuzzy switching surface function is put forward, which contains singular perturbation matrix and state-dependent input matrix simultaneously. Its corresponding sliding mode dynamics is a transformed fuzzy SPSs such that the matched uncertainty/perturbation is completely compensated without amplifying the unmatched one. By adopting a ϵ-dependent Lyapunov function, sufficient conditions are presented to guarantee the asymptotic stability of sliding mode dynamics, and a simple search algorithm is provided to find the stability bound. Then, a fuzzy SMC law is synthesized to ensure the reaching condition despite matched/unmatched uncertainties. A modified adaptive fuzzy SMC law is further constructed for adapting the unknown upper bound of the matched uncertainty. The applicability and superiority of obtained fuzzy SMC methodology are verified by a controller design for an electric circuit system.