H∞ and Robust Control of 2-D Systems in FM Second Model

  • Authors:

  • Lihua Xie;Chunling Du;Yeng Chai Soh;Cishen Zhang

  • Affiliations:

  • BLK S2, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 elhxie@ntu.edu.sg;MMS Group, Data Storage Institute, 5, Engineering Drive 1, Singapore 117608;BLK S2, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798;Department of Electrical and Electronic Engineering, The University of Melbourne, VIC 3010, Australia

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 2002

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Abstract

This paper deals with output feedback stabilization and H∞ control problems for two-dimensional (2-D) discrete linear systems without or with parameter uncertainty. The class of systems under investigation is described by the 2-D local state space Fornasini-Marchesini second model. We aim at designing a dynamical output feedback controller to achieve asymptotic stability and H∞ performance for the 2-D system. It is shown that the design of output feedback controller can be recast into a convex optimization problem characterized by linear matrix inequalities (LMIs). The LMI solution is further extended to solve the robust stabilization problem for 2-D systems subject to norm-bounded uncertainty. The solutions for the H∞ control and robust stabilization are applied to two application examples: thermal process control and robust stabilization of processes in Darboux equation.