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The design of reduced-order observer for Linear Parameter Varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parameterization of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on Linear Matrix Inequalities (LMIs) is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximization of the delay-margin or guaranteed suboptimal L 2-gain. Examples from the literature illustrate the efficiency of the approach.

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International audienceThe stabilization of uncertain LTI/LPV time-delay systems with time-varying delays by state-feedback controllers is addressed. Compared to other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow us to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, theH1 performance measure is considered. The interest of the approach is finally illustrated through several examples

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.