Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

Amit Dhawan

doi:10.4236/jsip.2012.32033

Abstract

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

Highlights

In the past decades, the two-dimensional (2-D) discrete systems have received much attention due to its practical and theoretical importance in the fields such as multidimensional digital filtering, image processing, seismographic data processing, thermal processes, gas absorption, water stream heating etc. [1,2,3,4]
This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model
In [15], the optimal guaranteed cost control problem for 2-D discrete uncertain systems described by the Roesser model has been discussed

Summary

Introduction

The two-dimensional (2-D) discrete systems have received much attention due to its practical and theoretical importance in the fields such as multidimensional digital filtering, image processing, seismographic data processing, thermal processes, gas absorption, water stream heating etc. [1,2,3,4]. Many significant results on the solvability of the stability problem for 2-D discrete systems described by the Roesser model [5] have been proposed in [6,7,8,9,10,11,12]. The non-fragile control problem for uncertain 2-D systems described by the Roesser model is an important problem. This paper, addresses the non-fragile robust stabilization problem for 2-D discrete uncertain systems described by the Roesser model. Stands for the matrix G is symmetric and negative definite

Problem Formulation and Preliminaries

Main Result

Numerical Example

Conclusion