Application of semi-definite programming to robust stability of delay systems

Abstract

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: • use of Padé approximation to transform the system into some singularly perturbed finite-dimensional system, for which robust dichotomy has to be checked; • recursive applications of Generalized Kalman–Yakubovich–Popov (KYP) lemma to characterise by an LMI the previous property.