Robust energy-to-peak filtering with improved LMI representations

The authors revisit the problem of robust energy-to-peak filtering for linear systems with parametric uncertainty residing in a polytope. Based on two results that appeared recently, they derive new L2–L∞ performance criteria which allow the use of parameter-dependent Lyapunov functions for analysis and synthesis problems. Robust L2–L∞ filters are then designed upon the new conditions and by means of the linear matrix inequality (LMI) technique, with the result that less conservativeness is achieved compared with earlier results that are based on a quadratic framework. Both continuous- and discrete-time cases are considered and numerical examples illustrate the feasibility and advantage of the proposed designs.