Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 50, Issue 12, Pages 2998-3007Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2002.805239
Keywords
H infinity filtering; linear matrix inequality; reduced-order filters; stochastic systems
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This paper deals with the reduced-order H-infinity filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any tank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.
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