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 ℋ₂ and/or ℋ_∞ norms are used as criteria in an estimation error sense. First, the optimal ℋ₂ filtering gain is obtained from the ℋ₂ norm state-space definition. Then the attenuation of arbitrary input signals is considered in an ℋ _∞ setting. Using the discrete-time version of the Bounded Real Lemma on the estimation error dynamics, a linear stable filter guaranteeing the optimal ℋ_∞ attenuation level is achieved. Finally, the central ℋ_∞ filter problem is solved, yielding a compromise between the preceding filter designs. All these filter design problems are formulated in a new convex optimization framework using LMIs. A numerical example is presented