Journal Article

A new Lyapunov technique for robust control of systems with uncertain non-small delays

Emilia Fridman

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 2, pages 165-179
Published in print June 2006 | ISSN: 0265-0754
Published online June 2006 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni051
A new Lyapunov technique for robust control of systems with uncertain non-small delays

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Stability, L2-gain analysis and state-feedback H control of linear systems with uncertain time-varying delays are considered in the case, where the nominal values of delays are constant and non-zero. A new construction of Lyapunov–Krasovskii functionals (LKFs) is introduced: to a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present paper we apply the nominal Lyapunov–Krasovskii functional (LKF) which is based on the descriptor model transformation. Sufficient conditions are given in terms of linear matrix inequalities. Numerical examples illustrate the efficiency of the method.

Keywords: uncertain delay; Lyapunov–Krasovskii method; stability; LMI; H∞ control

Journal Article.  0 words. 

Subjects: Mathematics

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