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

This paper addresses the problem of sliding mode control (SMC) for a type of uncertain time-delay nonlinear descriptor systems represented by T-S fuzzy models. One crucial contributing factor is to put forward a novel integral fuzzy switching manifold involved with time delay. Compared with previous results, the key benefit of the new manifold is that the input matrices via different subsystems are permitted to be diverse, and thus much more applicability will be achieved. By resorting to Frobenius' theorem and double orthogonal complement, the existence condition of the fuzzy manifold is presented. The admissibility conditions of sliding motion with a strictly dissipative performance are further provided. Then, the desired fuzzy SMC controller is synthesized by analyzing the reachability of the manifold. Moreover, an adaptive fuzzy SMC controller is also proposed to adapt the input saturation and the matched uncertainty with unknown upper bounds. The feasibility and virtue of our theoretical findings are demonstrated by a fuzzy SMC controller implementation for a practical system about the pendulum.

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In order to optimize traditional fault diagnosis models for practical applications, a fault diagnosis model based on support vector machines optimized with the adaptive quantum differential evolution of (AQDE-SVM) is proposed in this study. First, the traditional differential evolution is rewritten based on real number encoded into a qubit encoding. Second, this study proposes an adaptive quantum rotation gate and uses this gate to update the probability amplitude of the qubits. Finally, compared with quantum genetic algorithm support vector machines (QGA-SVM) and differential evolution-support vector machines (DE-SVM), etc., the results show that the algorithm proposed in this study has a higher diagnosis accuracy and shorter running time, providing great practical engineering value in the application of rolling bearing fault diagnosis.