Brief H∞ control and robust stabilization of two-dimensional systems in Roesser models

Authors:
Chunling Du;Lihua Xie;Cishen Zhang
Affiliations:
School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Vic. 3052, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

Feedback control of two-dimensional (2-D) systems is a problem of considerable importance in both theory and practical applications. In this paper, we present a state-space solution to the problem of H"~ control of 2-D systems. For a linear discrete time 2-D system described by a 2-D state-space Roesser model, a 2-D dynamic output feedback controller is designed to achieve the closed-loop system asymptotic stability and a specified H"~ performance using a linear matrix inequality (LMI) approach. We further give a solution for robust stabilization of 2-D systems subject to a class of norm bounded uncertainties. The results are demonstrated by an application example of stabilization of processes expressed in a Darboux equation.