New approach to mixed H2/H∞ filtering for polytopic discrete-time systems

This paper revisits the problem of mixed H₂/H_∞ filtering for polytopic discrete-time systems. Differing from previous results in the quadratic framework, the filter design makes full use of the parameter-dependent stability idea: Not only is the filter dependent of the parameters (which are assumed to reside in a polytope and be measurable online), but in addition, the Lyapunov matrices are different for the entire polytope domain, as well as for different channels with respect to the mixed performances. These ideas are realized by introducing additional slack variables to the well-established performance conditions and by employing new bounding techniques, which results in a much less conservative filter design method. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method.