Journal Article

Robust <i>ℋ</i><sub>∞</sub> state feedback control of discrete-time systems with state delay: an LMI approach

V. J. S. Leite, S. Tarbouriech and P. L. D. Peres

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 3, pages 357-373
Published in print September 2009 | ISSN: 0265-0754
Published online August 2009 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnp018
Robust ℋ∞ state feedback control of discrete-time systems with state delay: an LMI approach

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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 -guaranteed costs and for the design of robust state feedback gains assuring an 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 ℋ∞ cost; uncertain systems; linear matrix inequalities; parameter-dependent Lyapunov functions

Journal Article.  0 words. 

Subjects: Mathematics

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