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Research Papers

Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

[+] Author and Article Information
Chang Duan

e-mail: cduan@ncsu.edu

Fen Wu

e-mail: fwu@eos.ncsu.edu
Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 12, 2012; final manuscript received July 13, 2013; published online August 23, 2013. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 135(6), 061013 (Aug 23, 2013) (10 pages) Paper No: DS-12-1370; doi: 10.1115/1.4025027 History: Received November 12, 2012; Revised July 13, 2013

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples.

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Figures

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Fig. 1

The switched filtering system structure

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Fig. 2

Approximation of the norm-bounded uncertain set

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Fig. 3

Continuous-time switched H∞ filtering trajectories for a fixed uncertainty (a) z vs. zf, (b) estimation error e = z - zf, and (c) active filter index

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Fig. 4

Continuous-time switched H∞ filtering trajectories for a time-varying uncertainty (a) ϕ(t), (b) z vs. zf, (c) estimation error e = z - zf, and (d) active filter index

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Fig. 5

Simulation results of the semi-active suspension system (a) ϕ1(t) and ϕ2(t), (b) disturbance (road acceleration), (c) integral of e2(t), and (d) active filter index

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Fig. 6

Discrete-time switched H∞ filtering trajectories for a fixed uncertainty (a) z vs. zf, (b) estimation error e = z - zf, and (c) active filter index

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Fig. 7

Discrete-time switched H∞ filtering system trajectories for a time-varying uncertainty (a) ϕ(t), (b) z vs. zf, (c) estimation error e = z - zf, and (d) active filter index

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