Fuzzy [Formula: see text] output-feedback control for the discrete-time system with channel fadings, sector nonlinearities, and randomly occurring interval delays and nonlinearities.

Manfeng Hu,Yan Wang,Xiaozheng Fan

doi:10.1186/s13662-016-0991-3

Abstract

In this paper, the fuzzy H_{infty} output-feedback control problem is investigated for a class of discrete-time T-S fuzzy systems with channel fadings, sector nonlinearities, randomly occurring interval delays (ROIDs) and randomly occurring nonlinearities (RONs). A series of variables of the randomly occurring phenomena obeying the Bernoulli distribution is used to govern ROIDs and RONs. Meanwhile, the measurement outputs are subject to the sector nonlinearities (i.e. the sensor saturations) and we assume the system output is y(k)=0, kin{-l,ldots, 0}. The Lth-order Rice model is utilized to describe the phenomenon of channel fadings by setting different values of the channel coefficients. The aim of this work is to deal with the problem of designing a full-order dynamic fuzzy H_{infty} output-feedback controller such that the fuzzy closed-loop system is exponentially mean-square stable and the H_{infty} performance constraint is satisfied, by means of a combination of Lyapunov stability theory and stochastic analysis along with LMI methods. The proposed fuzzy controller parameters are derived by solving a convex optimization problem via the semidefinite programming technique. Finally, a numerical simulation is given to illustrate the feasibility and effectiveness of the proposed design technique.

Highlights

1 Introduction It is well known that the complexity and nonlinearity of the models are considered as ubiquitous in practical systems. The emergence of this fuzzy modeling approach is based on the Takagi-Sugeno (T-S) fuzzy system, which provides a powerful tool for modeling complex nonlinear systems
5 Conclusions In this paper, a fuzzy H∞ output-feedback controller has been designed for a class of fuzzy discrete-time systems with sector nonlinearities, channel fadings, randomly occurring interval delays as well as randomly occurring nonlinearities
A sufficient condition for the H∞ robust exponential stability of the fuzzy discrete-time system has been obtained by a Lyapunov stability analysis approach and stochastic analysis theory

Summary

Introduction

It is well known that the complexity and nonlinearity of the models are considered as ubiquitous in practical systems. In [ ], the H∞ output-feedback control problem for a class of discrete-time systems with channel fadings and sector nonlinearities has been studied, and the existence of the desired controllers has been derived via using a combination of the stochastic analysis and Lyapunov function approach. To the best of the authors’ knowledge, the fuzzy H∞ output-feedback control problem for a class of discrete-time T-S fuzzy system with channel fadings, sector nonlinearities, ROIDs and RONs have not been investigated yet, and the main purpose of this paper is to bridge such a gap. Motivated by the above discussion, this paper intends to study the fuzzy H∞ outputfeedback control problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy model system with channel fadings, sector nonlinearities, ROIDs, and RONs. The rest of this paper is organized as follows.

Model description and preliminaries

Conclusions