Parameter dependent state-feedback control of LPV time delay systems with time varying delays using a projection approach

Abstract

This paper is concerned with the stabilization of LPV time delay systems with time varying delays by parameter dependent state-feedback. First a stability test with H∞ performance is given through a parameter dependent LMI. This stability test is derived from a parameter dependent Lyapunov-Krasovskii functional combined with the Jensen's inequality. From this result we derive a state-feedback existence lemma expressed through a nonlinear matrix inequality (NMI). Using a result of the paper we are able to turn this (NMI) into a bilinear matrix inequality (BMI) involving a ‘slack’ variable. This BMI formulation is shown to be more flexible than the initial NMI formulation and is more adequate to be solved using algorithm such as ‘D-K iteration'. The controller construction is provided by two different ways. We finally discuss on the relaxation method and we show the efficiency of our method through several examples.