Resilient L ₂ – L ∞ filtering of polytopic systems with state delays

The problem of designing a resilient L2–L∞ filter for a class of linear uncertain state delay systems with uncertainties that belong to a convex-bounded polytopic domain is investigated. The objective is to derive tractable synthesis conditions for the resilient design of full-order and reduced-order filters such that a prescribed energy-to-peak disturbance-attenuation level is attained for all admissible uncertainties and gain perturbations. Both additive and multiplicative gain perturbations are considered. It is established that the filter design can be obtained from the solution of the convex optimisation problem over linear matrix inequalities. The design results are developed for both delay-independent and delay-dependent cases. In the latter case, two approaches are used: descriptor and extended Newton–Leibniz. Results on numerical simulations are presented to demonstrate the behaviour of the resilient filters.