Optimal filtering schemes for linear discrete-time systems - An LMI approach

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems, The transfer matrix H-2 and/or H-infinity norms are used as criteria in an estimation error sense. First, the optimal H-2 filtering gain is obtained from the H-2 norm state-space definition. Then the attenuation of arbitrary input signals is considered ih an H-infinity, setting. Using the discrete-time version of the Bounded Real Lemma on the estimation error dynamics, a linear stable filter guaranteeing the optimal H-infinity attenuation level is achieved. Finally, the central H-infinity filter problem is solved, yielding a compromise between the preceding fitter designs. All these filter design problems are formulated in a new convex optimization framework using LMIs. A numerical example is presented.