Brief paper: H2 and mixed H2/H∞ control of two-dimensional systems in Roesser model

Authors:
Ran Yang;Lihua Xie;Cishen Zhang
Affiliations:
School of Information Science and Technology, Sun Yat-Sen University, Guangzhou 510275, PR China;School of Electrical and Electronic Engineering, BLK S2, Nanyang Technological University, Singapore 639798, Singapore;School of Electrical and Electronic Engineering, BLK S2, Nanyang Technological University, Singapore 639798, Singapore
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

The H"2 performance specification for one-dimensional (1-D) systems has been known to be analytically and practically meaningful and widely applied to the analysis and design of control and signal processing systems. However, there has been few results on the analysis and design of two-dimensional (2-D) systems using the H"2 performance specification due to the structural and dynamical complexity of 2-D systems. In this paper, we extend the classical definition of the H"2 performance to 2-D systems and present a sufficient condition for evaluation of the H"2 performance of 2-D systems in Roesser model. Using this condition and the existing bounded real lemma, we develop systematic design methods for H"2 and mixed H"2/H"~ control of 2-D systems, and an application of the controller design methods to the control problem of a metal rolling process is demonstrated in this paper.