Dissipative filtering for linear discrete-time systems via LMI

The problem of the dissipative filtering for linear discrete systems is dealt with. A sufficient condition for existence of a dissipative filter such that the error filtering system is asymptotically stable and guarantees dissipative performance, are derived in the sense of Lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities (LMIs). Numerical example is provided to demonstrate the feasibility of the proposed condition and filters design procedure.