Extended parameter-dependent H∞ filtering for uncertain continuous-time state-delayed systems

The design of robust H-infinity filtering problem of polytopic uncertain linear time-delay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameter-dependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H-infinity performance level for all admissible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. An extended H-infinity sufficient condition for the existence of robust estimators is formulated in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.