Optimal filtering schemes for linear discrete-time systems: a linear matrix inequality approach

Abstract

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_infin; norms are used as criteria in an estimation error sense. First, the optimal filtering gain is obtained from the H ₂ 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 mixed H ₂ / 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 linear matrix inequalites. A numerical example is presented

Additional information

Notes on contributors

PEDRO L. D. PERES

Author to whom correspondence should be addressed: Fax: ( 55) 19 289 13 95; e-mail: { reinaldo} { pcres}@ dt. fee.unicamp. br