Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

Abstract

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H ∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example. Index Terms-Interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, persistent dwell-time (PDT) switching rule, quantized control, singularly perturbed nonlinear systems. I. INTRODUCTION S OME parasitic parameters, such as small time constants, capacitances, and inductances, may increase the order of dynamic equations and lead to the numerical ill-conditioning problem. In order to overcome these obstacles, the singular perturbation technique is usually employed. Examples of singularly perturbed systems (SPSs) are power systems, airplanes, and so on [1]-[3]. When discretizing continuous-time SPSs, the sampling period influences the discrete-time model, which

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