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IMA Journal of Mathematical Control and Information Advance Access originally published online on August 24, 2009
IMA Journal of Mathematical Control and Information 2009 26(3):357-373; doi:10.1093/imamci/dnp018
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Robust HFormula state feedback control of discrete-time systems with state delay: an LMI approach

V. J. S. Leite

CEFET-MG/Campus Divinópolis Rua Monte Santo, 319, Divinópolis 35502-036, MG, Brazil

S. Tarbouriech

LAAS-CNRS, Université de Toulouse, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex 4, France

P. L. D. Peres{dagger}

DT-FEEC-UNICAMP, University of Campinas CP 6101, Campinas 13081-970, SP, Brazil

{dagger} Email: peres{at}dt.fee.unicamp.br

Received on May 10, 2007; Accepted on April 5, 2008

In this paper, uncertain discrete-time systems with delayed states are investigated. The uncertainty is supposed to belong to a known convex polytope and can affect all system matrices. Sufficient linear matrix inequality conditions are given for the computation of HFormula-guaranteed costs and for the design of robust state feedback gains assuring an HFormula attenuation level. The conditions proposed here can assure robustness irrespective of the value of the delay and, differently from other approaches in the literature, are formulated as convex optimization problems. If the delay is known and the delayed states are available, a feedback gain depending on past values of the state can be used to improve the closed-loop performance of the system. As illustrated by numerical examples, including the model of an industrial electric heater, the proposed techniques are simple to be applied and can lead to less conservative results when compared with other conditions from the literature.

Keywords: timedelay; discrete-time systems; robust stability; guaranteed HFormula cost; uncertain systems; linear matrix inequalities; parameter-dependent Lyapunov functions.


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