H∞ control for discrete-time linear systems with Frobenius norm-bounded uncertainties

Authors:
El-Kébir Boukas;Peng Shi
Affiliations:
Departement de Genie Mecanique, Ecole Polytechnique de Montreal, Case Postale 6079, Succ. Centre-Ville, Montreal, Quebec, Canada H3C 3A7;Centre for Industrial and Applicable Mathematics, School of Mathematics, The University of South Australia, The Levels Campus, Mawson Lakes, SA 5095, Australia
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

In this paper, we consider the problems of robust stability and control for the class of uncertain discrete-time linear systems with Frobenius norm-bounded parameter uncertainties in all matrices of the system and output equations. Necessary and sufficient conditions for the above problems are proposed. A linear static state feedback control law is designed, which is in terms of a Riccati inequality. The results obtained here show that the robust control problem of the uncertain system is equivalent to the control problem for a corresponding uncertainty-free system.