Mixed H ₂/H _∞ filtering for a class of high-speed sampling uncertain systems

The problem of mixed H ₂/H _∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H ₂/H _∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H ₂/H _∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.