LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

Amit Dhawan,Haranath Kar

doi:10.4236/jsip.2011.24042

Abstract

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Highlights

In the past few years, due to the rapid increase of a wide variety of applications of two-dimensional (2-D) discrete systems in many practical application domains such as digital filtering, image and video processing, seismographic data processing, thermal processes, gas absorption, water stream heating, control systems etc. [1,2,3,4,5,6,7,8,9,10], there has emerged a continuously growing interest in the system theoretic problems of 2-D discrete systems
This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties
A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function

Summary

Introduction

In the past few years, due to the rapid increase of a wide variety of applications of two-dimensional (2-D) discrete systems in many practical application domains such as digital filtering, image and video processing, seismographic data processing, thermal processes, gas absorption, water stream heating, control systems etc. [1,2,3,4,5,6,7,8,9,10], there has emerged a continuously growing interest in the system theoretic problems of 2-D discrete systems. In [42,43,44], the guaranteed cost control problem for 2-D discrete uncertain systems in FMSLSS setting has been considered and a robust controller design method has been established. Robust suboptimal guaranteed cost control for 2-D discrete uncertain systems in FMSLSS setting is an important problem. This paper, deals with the suboptimal guaranteed cost control problem for 2-D discrete uncertain systems described by FMSLSS model with norm-bounded uncertainties.

Problem Formulation and Preliminaries

A H F E T P A H F E Q 0

Main Result

M11 M1T2

Conclusions