A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

Yunsai Chen,Liang Ma,Yongjie Pang,Zhao Yang

doi:10.1155/2018/1875610

Abstract

This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust H∞ performance γ. By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

Highlights

Over the past few decades, hybrid systems have drawn tremendous attention from the control community, as they contain the competence to model the interaction between logic components and continuous dynamics [1,2,3,4,5,6]
This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models
Via employing a state-control augmentation approach, a new nonfragile controller synthesis method is proposed based on piecewise Lyapunov functions (PLFs), which removes the restrictive condition that the input matrices do not have uncertainties

Summary

Introduction

Over the past few decades, hybrid systems have drawn tremendous attention from the control community, as they contain the competence to model the interaction between logic components and continuous dynamics [1,2,3,4,5,6]. The authors in [20] designed a static output-feedback controller for discrete-time PWA systems such that the resulting closed-loop system was asymptotically stable with robust H∞ performance γ. In spite of the attractive features in piecewise affine systems, the authors in [41] proposed a state-feedback nonfragile robust controller design method for continuoustime PWA systems. Via employing a state-control augmentation approach, a new nonfragile controller synthesis method is proposed based on piecewise Lyapunov functions (PLFs), which removes the restrictive condition that the input matrices do not have uncertainties. This feature enables one to design the nonfragile controller for a broader class of industrial systems. A real symmetric matrix A > 0(≥ 0) indicates A being positive-definite (positive-semi-definite). sym{X} is the shorthand notation for XT + X

Problem Formulation

Piecewise Affine Nonfragile Controller Analysis and Design

Simulation

Conclusion