H2 robust filter design with performance certificate via convex programming

In this paper a new approach to H2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H2 robust filter design, a new one based...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 44; no. 4; pp. 937 - 948
Main Authors: Geromel, José C., Korogui, Rubens H.
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.04.2008
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Convex programming
Exact sciences and technology
Filter design
Kalman filter
Linear matrix inequalities (LMIs)
Robust [formula omitted] filtering
Linear matrix inequalities (LMIs)
Filter design
Convex programming
Kalman filter
Robust H2 filtering
Polytope
Lower bound
Estimation error
Error estimation
Continuous time
Robust control
Upper bound
Uncertain system
Linear filter
Minimax problem
Discrete time
Linear matrix inequality
Causality
Invarying system
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:In this paper a new approach to H2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2007.08.010