Design of LPV observers for LPV time-delay systems: an algebraic approach

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 L2-gain. Examples from the literature illustrate the efficiency of the approach.