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Robust mixed ℋ2/ℋ filtering design for discrete-time switched polytopic linear systems

Robust mixed ℋ2/ℋ filtering design for discrete-time switched polytopic linear systems

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The authors deal with mode and parameter-dependent robust mixed ℋ2/ℋ filtering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed ℋ2/ℋ filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust ℋ2 and ℋ performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

References

    1. 1)
      • R.A. Decarlo , M.S. Branchy , S. Pettersson , B. Lennartson . Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE , 7 , 1069 - 1082
    2. 2)
      • D. Liberzon , A.S. Morse . Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. , 5 , 59 - 70
    3. 3)
      • Peleties, P., Decarlo, R.A.: `Asymptotic stability of m-switched systems using Lyapunov-like functions', Proc. 1991 American Control Conf, 1991, Boston, MA, p. 1679–1684.
    4. 4)
      • M.S. Branicky . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control , 4 , 475 - 482
    5. 5)
      • H. Ye , A.N. Michel , L. Hou . Stability theory for hybrid dynamical systems. IEEE Trans. Autom. Control , 4 , 461 - 474
    6. 6)
      • J. Daafouz , P. Riedinger , C. Iung . Stability and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control , 11 , 1883 - 1887
    7. 7)
      • Fang, L., Lin, H., Antsaklis, P.J.: `Stabilization and performance analysis for a class of switched systems', Proc. 43rd IEEE Conf. Decision and Control, 2004, p. 3265–3270.
    8. 8)
      • D. Xie , L. Wang , F. Hao , G. Xie . LMI approach to L2-gain analysis and control synthesis of uncertain switched systems. IEE Proc. Control Theory Appl. , 1 , 21 - 28
    9. 9)
      • Gao, H., Zhang, L., Shi, P., Mou, S., Wang, C.: `Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties', Proc. 2006 American Control Conf., 2006, Minnesota, USA, p. 5953–5958.
    10. 10)
      • H. Gao , J. Lam , C. Wang . Model simplification for switched hybrid systems. Syst. Control Lett. , 12 , 1015 - 1021
    11. 11)
      • L. Zhang , P. Shi , C. Wang , H. Gao . Robust ℋ∞ filtering for switched linear discrete-time systems with polytopic uncertainties. Int. J. Adaptive Control Signal Process. , 6 , 291 - 304
    12. 12)
      • L. Zhang , P. Shi , E.-K. Boukas , C. Wang . Robust l2−l∞ filtering for switched linear discrete time-delay systems with polytopic uncertainties. IET Control Theory Appl. , 3 , 722 - 730
    13. 13)
      • D. Du , B. Jiang , P. Shi , S. Zhou . ℋ∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control , 8 , 1520 - 1525
    14. 14)
      • C. Farges , D. Peaucelle , D. Arzelier , J. Daafouz . Robust ℋ2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Syst. Control Lett. , 2 , 159 - 166
    15. 15)
      • H. Li , M. Fu . A linear matrix inequality approach to robust ℋ∞ filtering. IEEE Trans. Signal Process. , 9 , 2338 - 2350
    16. 16)
      • R.M. Palhares , P.L.D. Peres . Robust filtering with guaranteed energy-to-peak performance–an LMI approach. Automatica , 6 , 851 - 858
    17. 17)
      • H.D. Tuan , P. Apkarian , T.Q. Nguyen . Robust and reduced-order filtering: new LMI-based characterizations and methods. IEEE Trans. Signal Process. , 12 , 2975 - 2984
    18. 18)
      • Z. Wang , D.W.C. Ho , X. Liu . Robust filtering under randomly varying sensor delay with variance constraints. IEEE Trans. Circuits Syst. II, Express Briefs , 6 , 320 - 326
    19. 19)
      • L. Xie , L. Lu , D. Zhang , H. Zhang . Improved robust ℋ2 and ℋ∞ filtering for uncertain discrete-time systems. Automatica , 5 , 873 - 880
    20. 20)
      • C.E. De Souza , K.A. Barbosa , A.T. Neto . Robust ℋ∞ filtering for discrte-time linear systems with uncertain time-varying parameters. IEEE Trans. Signal Process. , 6 , 2110 - 2118
    21. 21)
      • Z. Duan , J. Zhang , C. Zhang , E. Mosca . A simple design method of reduced-order filters and its applications to multirate filter bank design. Signal Process. , 5 , 1061 - 1075
    22. 22)
      • Z. Duan , J. Zhang , C. Zhang , E. Mosca . Robust ℋ2 and ℋ∞ filtering for uncertain linear systems. Automatica , 11 , 1919 - 1926
    23. 23)
      • H. Gao , T. Chen . ℋ∞ estimation for uncertain systems with limited communication capacity. IEEE Trans. Autom. Control , 11 , 2070 - 2084
    24. 24)
      • H. Rotstein , M. Sznaier , M. Idan . ℋ2/ℋ∞ filtering theory and an aerospace application. Int. J. Robust Nonlinear Control , 4 , 347 - 366
    25. 25)
      • R.M. Palhares , P.L.D. Peres . LMI approach to the mixed ℋ2/ℋ∞ filtering design for discrete-time systems. IEEE Trans. Aerosp. Electron. Sys. , 1 , 292 - 296
    26. 26)
      • H. Gao , J. Lam , L. Xie , C. Wang . New approach to mixed ℋ2/ℋ∞ filtering for polytopic discrete-time systems. IEEE Trans. Signal Process. , 8 , 3183 - 3192
    27. 27)
      • H. Gao , J. Lam , P. Shi , C. Wang . Parameter-dependent filter design with guaranteed ℋ∞ performance. IEE Proc., Control Theory Appl. , 5 , 531 - 537
    28. 28)
      • W. Zhang , L. Yu , X. Jiang . Delay-dependent generalized ℋ2 filtering for uncertain systems with multiple time-varying state delays. Signal Process. , 4 , 709 - 724
    29. 29)
      • J. Qiu , G. Feng , J. Yang . Improved delay-dependent ℋ∞ filtering design for discrete-time polytopic linear delay systems. IEEE Trans. Circuits Syst. II, Express Briefs, to appear
    30. 30)
      • E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi . ℋ2/ℋ∞ filter design for systems with polytope-bounded uncertainty. IEEE Trans. Signal Process. , 9 , 3620 - 3626
    31. 31)
      • Leite, V.J.S., Montagner, V.F., Peres, P.L.D.: `Robust pole location by parameter-dependent state feedback control', Proc. 41st IEEE Conf. Decision and Control, 2002, Las Vegas, NV, p. 1864–1869.
    32. 32)
      • M.C. De Oliveira , R.E. Skelton , S.O. Reza Moheimani . (2001) Stability tests for constrained linear systems’, in Perspectives in robust control, Lecture Notes in Control and Information Scieneces.
    33. 33)
      • Z. Duan , J. Wang , L. Huang . Parameter-dependent Lyapunov function method for a class of uncertain nonlinear systems with multiple equilibria. Circuits Syst. Signal Process. , 2 , 147 - 164
    34. 34)
      • R.C.L.F. Oliveira , P.L.D. Peres . LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. Syst. Control Letters. , 1 , 52 - 61
    35. 35)
      • G. Chesi , A. Garulli , A. Tesi , A. Vicino . Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions. Automatica , 2 , 309 - 316
    36. 36)
      • E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi , R.C. Mesquita . New strategy for robust stability analysis of discrete-time uncertain systems. Syst. Control Lett. , 516 - 524
    37. 37)
      • E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi , R.C. Mesquita . ℋ2 and ℋ∞ ε-guaranteed cost computation of uncertain linear systems. IET Control Theory Appl. , 1 , 201 - 209
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