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Research Papers

Parameter-Dependent Filtering for Linear Time-Varying Systems

[+] Author and Article Information
Hui Zhang

e-mail: huizhang@uvic.ca

Yang Shi

e-mail: yshi@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055, STN CSC, BC, V8W 3P6, Canada

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received January 11, 2011; final manuscript received July 13, 2012; published online November 7, 2012. Assoc. Editor: Bor-Chin Chang.

J. Dyn. Sys., Meas., Control 135(2), 021006 (Nov 07, 2012) (7 pages) Paper No: DS-11-1004; doi: 10.1115/1.4007553 History: Received January 11, 2011; Revised July 13, 2012

In this paper, we investigate the filter design problem for linear continuous-time systems with parameter variations in system matrices. The parameter variations are assumed to belong to a polytope with finite and known vertices. The designed filter parameters and the constructed Lyapunov function are both dependent on the online measured variations. A new sufficient condition for the existence of parameter-dependent filters is established and it can guarantee that the filtering error dynamic system is asymptotically stable and can satisfy the prescribed norm bound. Then, the design of the filter is proposed by solving a set of linear matrix inequalities (LMIs). Simulation studies and comparison examples are provided to illustrate the effectiveness of the proposed method.

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Figures

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Fig. 1

Singular value curves of the filtering error system transfer functions at the four vertices

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Fig. 2

Singular value curves of the filtering error system transfer functions at the two vertices

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Fig. 3

Bounded external disturbance used in this simulation

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Fig. 4

Estimation error comparison with different filters

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