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Application of semi-definite programming to robust stability of delay systems. (English) Zbl 1140.93034

Summary: We study here robust stability of linear systems with several uncertain incommensurate delays, more precisely the property usually called delay-dependent stability. The main result of this paper consists in establishing that the latter is equivalent to the feasibility of some Linear Matrix Inequality (LMI), a convex optimization problem whose numerical solution is well documented.
The method is based on two main techniques:
\(\bullet \) use of Padé approximation to transform the system into some singularly perturbed finite-dimensional system, for which robust dichotomy has to be checked,
\(\bullet \) recursive applications of Generalized Kalman-Yakubovich-Popov (KYP) lemma to characterise by an LMI the previous property.

MSC:

93D09 Robust stability
90C22 Semidefinite programming
93D20 Asymptotic stability in control theory
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C05 Linear systems in control theory
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