Robust L₂-L_∞ filtering for uncertain systems with multiple time-varying state delays

This paper is concerned with the robust L₂-L_∞ filtering problem for uncertain systems with multiple time-varying state delays. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed energy-to-peak noise-attenuation level for all admissible uncertainties and time delays. The admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Both delay-independent and dependent approaches are presented, with an example illustrating the validity of the proposed designs.