New Stabilization Results for Semi-Markov Chaotic Systems with Fuzzy Sampled-Data Control

Tao Wu,Haiyang Zhang,Lianglin Xiong,Jinde Cao

doi:10.1155/2019/7875305

Abstract

This paper investigates the problem of stabilization for semi-Markov chaotic systems with fuzzy sampled-data controllers, in which the semi-Markov jump has generally uncertain transition rates. The exponential stability condition is firstly obtained by the following two main techniques: To make full use of the information about the actual sampling pattern, a novel augmented input-delay-dependent Lyapunov–Krasovskii functional (LKF) is firstly introduced. Meanwhile, a new zero-value equation is established to increase the combinations of component vectors of the resulting vector. The corresponding fuzzy sampled-data controllers are designed based on the stability condition. Finally, the validity and merits of the developed theories are shown by two numerical examples.

Highlights

As we all know, Takagi–Sugeno fuzzy model (T-SFM) [1] is an applicable and e ective way for us to approximate complex nonlinear systems
Input-delay-dependent Lyapunov terms with high-order function of input delay are difficultly contained because their derivation may be nonlinear input delay. en, the convex combination technique cannot be directly utilized. us, it is still a challenging issue to construct input-delay-dependent Lyapunov–Krasovskii functional (LKF) with high-order function of input delay to further improve the existing results for fuzzy sampled-data chaotic systems, which is the first motivation of this paper
(iii) To take full advantage of the available information with regard to the practical sampling mode, a new augmented time-dependent LKF V3(x(t), rt) is constructed, which is firstly presented for the fuzzy sampled-data semi-Markov chaotic systems

Summary

Introduction

Takagi–Sugeno fuzzy model (T-SFM) [1] is an applicable and e ective way for us to approximate complex nonlinear systems. Us, it is still a challenging issue to construct input-delay-dependent LKFs with high-order function of input delay to further improve the existing results for fuzzy sampled-data chaotic systems, which is the first motivation of this paper. Based on the above discussions, the aim of this paper is to further investigate the problem of stabilization for fuzzy chaotic systems with sampled-data control and semi-Markov jump of generally uncertain transition rates. (i) is discussion for chaotic systems with both fuzzy sampled-data control and semi-Markov jump of generally uncertain transition rates is for the first time to be proposed. (iii) To take full advantage of the available information with regard to the practical sampling mode, a new augmented time-dependent LKF V3(x(t), rt) is constructed, which is firstly presented for the fuzzy sampled-data semi-Markov chaotic systems. (iv) Compared with the existing stabilization conditions in [21, 24,25,26], our results are less computationally complex and less conservative

Problem Statement and Preliminaries

Numerical Simulation

Findings

Method