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

Corentin Briat (1) , Olivier Sename (1) , Jean-François Lafay (2)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

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-infinity 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.

Domaines: Automatique / Robotique

Corentin Briat, Olivier Sename, Jean-François Lafay. Parameter dependent state-feedback control of LPV time-delay systems with time-varying delays using a projection approach. IFAC WC 2008 - 17th IFAC World Congress, Jul 2008, Séoul, South Korea. ⟨hal-00336998⟩