Robust H∞ filtering design with pole constraints for discrete-time systems: an LMI approach

The problem of full order guaranteed cost H_∞ filtering design for discrete-time systems with polytope type uncertainty is investigated. The main purpose is to obtain a stable linear filter such that the filtering error system remains quadratically stable within a prespecified H_∞ attenuation level. Necessary and sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities (LMIs), which can be efficiently solved by means of high performance convex optimization procedures with global convergence assured. Moreover, as an improvement, the filter dynamics can be constrained to some specific regions inside the unit open disk