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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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References

Fridman, E., Shaked, U., and Xie, L., 2003, “Robust ℋ∞ Filtering of Linear Systems With Time-Varying Delay,” IEEE Trans. Autom. Control, 48(1), pp. 159–165. [CrossRef]
Elsayed, A., and Grimble, M. J., 1989, “A New Approach to the ℋ∞ Design of Optimal Digital Linear Filters,” IMA J. Math. Control Inf., 6(2), pp. 233–251. [CrossRef]
Duan, Z., Zhang, J., Zhang, C., and Mosca, E., 2006, “Robust ℋ∞ and ℋ∞ Filtering for Uncertain Linear Systems,” Automatica, 42(11), pp. 1919–1926. [CrossRef]
Wu, L., Wang, Z., Gao, H., and Wang, C., 2007, “ℋ∞ and l2-l∞ Filtering for Two-Dimensional Linear Parameter-Varying Systems,” Int. J. Robust Nonlinear Control, 17(12), pp. 1129–1154. [CrossRef]
McEneaney, W. M., 1998, “Robust/ℋ∞ Filtering for Nonlinear Systems,” Syst. Control Lett., 33(5), pp. 315–325. [CrossRef]
Lan, W., Chen, B. M., and Lewis, F. L., 2008, “Explicit Constructions of Global Stabilization and Nonlinear ℋ∞ Control Laws for a Class of Nonminimum Phase Nonlinear Multivariable Systems,” Int. J. Robust Nonlinear Control, 18(12), pp. 1257–1284. [CrossRef]
Yang, G.-H., and Dong, J., 2008, “ℋ∞ Filtering for Fuzzy Singularly Perturbed Systems,” IEEE Trans. Syst., Man, Cybern. Part B: Cybern., 38(5), pp. 1371–1389. [CrossRef]
Dong, H., Wang, Z., and Gao, H., 2010, “Robust ℋ∞ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts,” IEEE Trans. Signal Process., 58(4), pp. 1957–1966. [CrossRef]
Dong, H., Wang, Z., Ho, D. W. C., and Gao, H., 2010, “Variance-Constrained ℋ∞ Filtering for Nonlinear Time-Varying Stochastic Systems With Multiple Missing Measurements: The Finite-Horizon Case,” IEEE Trans. Signal Process., 58(5), pp. 2534–2543. [CrossRef]
Wang, Z., Yang, F., Ho, D. W. C., and Liu, X., 2006, “Robust ℋ∞ Filtering for Stochastic Time-Delay Systems With Missing Measurements,” IEEE Trans. Signal Process., 54(7), pp. 2579–2587. [CrossRef]
Zhang, X.-M., and Han, Q.-L., 2009, “A Less Conservative Method for Designing ℋ∞ Filters for Linear Time-Delay Systems,” Int. J. Robust Nonlinear Control, 19(12), pp. 1376–1396. [CrossRef]
Zhang, H., Dang, C., and Zhang, J., 2010, “Decentralized Fuzzy ℋ∞ Filtering for Nonlinear Interconnected Systems With Multiple Time Delays,” IEEE Trans. Syst., Man, Cybern. Part B: Cybern., 40(4), pp. 1197–1203. [CrossRef]
Zhang, H., Saadat Mehr, A., and Shi, Y., 2010, “Improved Robust Energy-to-Peak Filtering for Uncertain Linear Systems,” Signal Process., 90(9), pp. 2667–2675. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2010, “Robust Energy-to-Peak Filtering for Networked Systems With Time-Varying Delays and Randomly Missing Data,” IET Control Theory Appl., 4(12), pp. 2921–2936. [CrossRef]
Apkarian, P., and Gahinet, P., 1995, “A Convex Characterization of Gain-Scheduled ℋ∞ Controllers,” IEEE Trans. Autom. Control, 40(5), pp. 853–864. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2011, “Robust Non-Fragile Dynamic Vibration Absorbers With Uncertain Factors,” J. Sound Vib., 330(4), pp. 559–566. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2011, “Robust Weighted ℋ∞ Filtering for Networked Systems With Intermitted Measurements of Multiple Sensors,” Int. J. Adapt. Control Signal Process., 25(4), pp. 313–330. [CrossRef]
Zhang, H., Shi, Y., Saadat Mehr, A., and Huang, H., 2011, “Robust Energy-to-Peak FIR Equalization for Time-Varying Communication Channels With Intermittent Observations,” Signal Process., 91(7), pp. 1651–1658. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2011, “Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems,” IEEE Trans. Ind. Electron., 58(12), pp. 5396–5405. [CrossRef]
Yan, M., and Shi, Y., 2008, “Robust Discrete-Time Sliding Mode Control for Uncertain Systems With Time-Varying State Delay,” IET Control Theory Appl., 2(8), pp. 662–674. [CrossRef]
Barbosa, K. A., de Souza, C. E., and Trofino, A., 2005, “Robust ℋ2 Filtering for Uncertain Linear Systems: LMI Based Methods With Parametric Lyapunov Functions,” Syst. Control Lett., 54(3), pp. 251–262. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “Robust ℋ∞ PID Control for Multivariable Networked Control Systems With Disturbance/Noise Attenuation,” Int. J. Robust Nonlinear Control, 22(2), pp. 183–204. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “On ℋ∞ Filtering for Discrete-Time Takagi-Sugeno Fuzzy Systems,” IEEE Trans. Fuzzy Syst., 20(2), pp. 396–401. [CrossRef]
Gao, H., Meng, X., and Chen, T., 2008, “New Design of Robust ℋ∞ for 2-D Systems,” IEEE Signal Process. Lett., 15(6), pp. 217–220. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “Robust Equalisation for Inter Symbol Interference Communication Channels,” IET Signal Process., 6(2), pp. 73–78. [CrossRef]
Zhang, J., Xia, Y., and Shi, P., 2009, “Parameter-Dependent Robust ℋ∞ Filtering for Uncertain Discrete-Time Systems,” Automatica, 45(2), pp. 560–565. [CrossRef]
Borges, R. A., Montagner, V. F., Oliveira, R. C. L. F., Peres, P. L. D., and Bliman, P. A., 2008, “Parameter-Dependent ℋ2 and ℋ∞ Filter Design for Linear Systems With Arbitrarily Time-Varying Parameters in Polytopic Domains,” Signal Process., 88(7), pp. 1801–1816. [CrossRef]
de Oliveira, M. C., Bernussou, J., and Geromel, J. C., 1999, “A New Discrete-Time Robust Stability Condition,” Syst. Control Lett., 37(4), pp. 261–265. [CrossRef]
Oliveira, R. C. L. F., and Peres, P. L. D., 2006, “LMI Conditions for Robust Stability Analysis Based on Polynomially Parameter-Dependent Lyapunov Functions,” Syst. Control Lett., 55(1), pp. 52–61. [CrossRef]
Zhang, B., Lam, J., and Xu, S., 2009, “Deconvolution Filtering for Stochastic Systems via Homogeneous Polynomial Lyapunov Functions,” Signal Process., 89(4), pp. 605–614. [CrossRef]
Gao, H., Meng, X., and Chen, T., 2009, “ℋ∞ Filter Design for Discrete Delay Systems: A New Parameter-Dependent Approach,” Int. J. Control, 82(6), pp. 993–1005. [CrossRef]
Gao, H., Lam, J., Xie, L., and Wang, C., 2005, “New Approach to Mixed ℋ2/ℋ∞ Filtering for Polytopic Discrete-Time Systems,” IEEE Trans. Signal Process, 53(8), pp. 3183–3192. [CrossRef]
Qiu, J., and Feng, G., 2008, “Improved Delay-Dependent ℋ∞ Filtering Design for Discrete-Time Polytopic Linear Delay Systems,” IEEE Trans. Circuits Syst. II: Express Briefs, 55(2), pp. 178–182. [CrossRef]
Gao, H., and Chen, T., 2007, “ℋ∞ Estimation for Uncertain Systems With Limited Communication Capacity,” IEEE Trans. Autom. Control, 52(11), pp. 2070–2084. [CrossRef]
Yu, B., Shi, Y., and Huang, H., 2008, “l2-l∞ Filtering for Multirate Systems Based on Lifted Models,” Circuits Syst. Signal Process., 27(5), pp. 699–711. [CrossRef]
Shaked, U., 1990, “ℋ∞-Minimum Error State Estimation of Linear Stationary Processes,” IEEE Trans. Autom. Control, 35(5), pp. 554–558. [CrossRef]
Xie, L., Lu, L., Zhang, D., and Zhang, H., 2004, “Improved Robust ℋ2 and ℋ∞ Filtering for Uncertain Discrete-Time Systems,” Automatica, 40(5), pp. 873–880. [CrossRef]
Gao, H., Meng, X., and Chen, T., 2008, “A New Design of Robust ℋ2 Filters for Uncertain Systems,” Syst. Control Lett., 57(7), pp. 585–593. [CrossRef]
Palhares, R. M., and Peres, P. L. D., 2000, “Robust Filtering With Guaranteed Energy-to-Peak Performance—An LMI Approach,” Automatica, 36(6), pp. 851–858. [CrossRef]
Gao, H., Lam, J., and Wang, C., 2006, “Robust Energy-to-Peak Filter Design for Stochastic Time-Delay Systems,” Syst. Control Lett., 55(2), pp. 101–111. [CrossRef]
Zhang, L., Shi, P., Boukas, E. K., and Wang, C., 2007, “Robust l2-l∞ Filtering for Switched Linear Discrete Time-Delay Systems With Polytopic Uncertainties,” IET Control Theory Appl., 1(3), pp. 722–730. [CrossRef]
de Oliveira, M. C., 2004, “Investigating Duality on Stability Conditions,” Syst. Control Lett., 52(1), pp. 1–6. [CrossRef]
Gao, H., Yang, X., and Shi, P., 2009, “Multi-Objective Robust ℋ∞ Control of Spacecraft Rendezvous,” IEEE Trans. Control Syst. Technol., 17(4), pp. 794–802. [CrossRef]
Yang, X., Gao, H., Shi, P., and Duan, G., 2010, “Robust ℋ∞ Control for a Class of Uncertain Mechanical Systems,” Int. J. Control, 83(7), pp. 1303–1324. [CrossRef]
Zhang, H., and Shi, Y., 2012, “Delay-Dependent Stabilization of Discrete-Time Systems With Time-Varying Delay via Switching Technique,” ASME J. Dyn. Sys., Meas., Control, 134(4), p. 044503. [CrossRef]
Wu, J., Zhang, H., and Shi, Y., 2012, “ℋ2 State Estimation for Network-Based Systems Subject to Probabilistic Delays,” Signal Process., 92(11), pp. 2700–2706. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Bounded external disturbance used in this simulation

Grahic Jump Location
Fig. 4

Estimation error comparison with different filters

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