A new method for robust H∞ filtering of uncertain discrete-time systems

This paper deals with the robust H_∞ filtering problem for discrete-time linear systems with polytopic uncertainties. Differently from existing results, we assume that not only the Lyapunov functions are parameter-dependent in the whole polytope domain, but also the filter is dependent of the parameters which belong to a polytope. Our results contain no constant matrix variable for the entire polytope domain, which guarantees to provide extra free dimensions in the solution space for the H_∞ filtering problem and establish less conservative filter design method. In addition, the robust H_∞ filter can be established by linear matrix inequalities (LMIs) which can be solved numerically by efficient convex optimization techniques. The effectiveness of the proposed design methods is finally verified by a numerical example at the end of the paper.