Technical communique: Design of state estimators for uncertain linear systems using quadratic boundedness

Authors:
Angelo Alessandri;Marco Baglietto;Giorgio Battistelli
Affiliations:
Department of Production Engineering, Thermoenergetics, and Mathematical Models, DIPTEM-University of Genoa, P. le Kennedy Pad. D, 16129 Genova, Italy;Department of Communications, Computer and System Sciences DIST-University of Genoa, Via Opera Pia 13, 16145 Genova, Italy;Department of Communications, Computer and System Sciences DIST-University of Genoa, Via Opera Pia 13, 16145 Genova, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

The notion of quadratic boundedness, which allows one to address the stability of a dynamic system in the presence of bounded disturbances, is applied to the design of state estimators for discrete-time linear systems with polytopic uncertainties. Necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived. For the purpose of design, such conditions can be expressed in terms of linear matrix inequalities (LMIs), thus guaranteeing the numerical tractability. Simulation results are reported to show the effectiveness of the approach.