Delay-dependent generalized H2 filtering for uncertain systems with multiple time-varying state delays

A delay- and parameter-dependent approach to generalized H2 filtering is proposed for linear continuous-time uncertain systems with multiple time-varying state delays. The uncertain parameters are assumed to reside in a polytope, and the aim is to design a parameter-dependent or a parameter-independent filter such that the filtering error systems are assured to be asymptotically stable and a prescribed generalized H2 performance is guaranteed. The proposed filter design method possesses many advantages, such as the reduced conservatism of the obtained delay-dependent criteria due to adopting the newly established integral-inequality; the proposed new linearization technique and the parameter-dependent design method for the parameter-dependent filters. Both the conditions for the existence of the parameter-dependent and parameter-independent filters are presented in terms of linear matrix inequalities, and convex optimization problems are formulated to design the desired filters. A numerical example is given to illustrate the validity of the proposed design.