Dynamic Sliding-Mode Control for T-S Fuzzy Singular Time-Delay Systems With ${H}_{\infty}$ Performance

Jiasheng Shi,Qingling Zhang

doi:10.1109/access.2019.2935456

Jiasheng Shi, Qingling Zhang

Open Access

https://doi.org/10.1109/access.2019.2935456

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Abstract

In this paper, we propose a novel sliding-mode control for Takagi-Sugeno (T-S) fuzzy singular system with time-delay and mismatched uncertainties and disturbances. In the majority of T-S fuzzy sliding-mode control ways, a restrictive assumption is required, that is every subsystem's input matrix is identical. In order to eliminate the restrictive assumption, we put forward a dynamic sliding-mode control method for T-S fuzzy singular time-delay systems. Additionally, the dynamic sliding-mode control law is designed to guarantee the reachability of the sliding surface in finite time interval. Stability of sliding motion is analyzed and the dynamic sliding-mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. In the end, three examples are shown to verify the merit and effectiveness of the proposed approaches are provided.

Highlights

Since the 1980s, T-S fuzzy models have attracted great interest from the control community, because of their effectiveness in approximating the complex nonlinear systems [1]
The admissibility, the paper [11] was the first to give the sufficient conditions for the T-S fuzzy singular systems
DESIGN OF DYNAMIC SLIDING-MODE CONTROL we focus on the dynamic sliding-mode control (DSMC) design and the admissibility of the sliding motion

Summary

INTRODUCTION

Since the 1980s, T-S fuzzy models have attracted great interest from the control community, because of their effectiveness in approximating the complex nonlinear systems [1]. To the authors’ best knowledge, in the current literature, few effective results on removing the constraint assumption for the T-S fuzzy singular systems with SMC [28]. Most of the papers study T-S fuzzy systems via SMC with matched uncertainties and disturbances [24], [26]–[28]. This paper researches a dynamic sliding-mode control (DSMC) strategy for a class of T-S fuzzy singular time-delay systems subject to mismatched norm-bounded uncertainties and disturbances. The dynamic sliding-mode control for T-S fuzzy singular time-delay systems with the mismatched disturbances is shown in Fig.. 1. A novel dynamic sliding-mode controller is designed to stabilize the T-S fuzzy singular time-delay systems.

SYSTEM DESCRIPTION AND PRELIMINARIES

SIMULATION EXAMPLES

DSMC Technique

CONCLUSION