An LMI approach to H∞ filtering of uncertain systems

This paper studies the H_∞ filtering problem of linear uncertain systems with polytopic uncertainties. By introducing some slack matrices and using the parameter-dependent Lyapunov function approaches, sufficient conditions for the existence of such filter are expressed in terms of linear matrix inequalities (LMIs). And, a convex analysis procedure is implemented to derive the filter gain matrices. Finally, a numerical example is presented to illustrate the theoretical developments.