On multiobjective synthesis for parameter-dependent descriptor systems

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This note proposes dilated (or extended) linear matrix inequality (LMI) characterisations of admissibility, D-admissibility, H∞ and H2 norms for continuous-time descriptor systems. As for state-space systems, these LMIs achieve less conservative results when dealing with robust admissibility/performance analysis of affine parameter-dependent descriptor systems. Furthermore, an iterative design procedure for multiobjective state-feedback control of parameter-dependent descriptor systems is presented based on these dilated LMI conditions. The main idea underlying the proposed method is to linearise the products of controller parameter and the auxiliary variable by assigning the last one. In the initialisation step of the proposed algorithm, the assignment takes into account an explicit characterisation of the auxiliary variable. The effectiveness of the proposed conditions and design method is shown through some numerical examples.

Inspec keywords: linear matrix inequalities; continuous time systems; state-space methods; state feedback

Other keywords: multiobjective state feedback control; affine parameter-dependent descriptor systems; D-admissibility; state-space systems; H infinity; continuous time descriptor systems; robust admissibility; iterative design procedure; multiobjective synthesis; linear matrix inequality characterisations; performance analysis

Subjects: Control system analysis and synthesis methods; Linear algebra (numerical analysis)

References

    1. 1)
      • J.Y. Ishihara , M.H. Terra . On the Lyapunov theorem for singular systems. IEEE Trans. Autom. Control , 11 , 1926 - 1930
    2. 2)
      • Marx, B., Koenig, D., Georges, D.: `Robust pole-clustering for descriptor systems a strict LMI characterization', Proc. European Control Conf., 2003.
    3. 3)
      • T. Shimomura , T. Fujii . Multiobjective control via successive over-bounding of quadratic terms. Int. J. Robust Nonlinear Control , 363 - 381
    4. 4)
      • A. Kumar , P. Daoutidis . (1999) Control of nonlinear differential algebraic equation systems.
    5. 5)
      • Takaba, K., Katayama, T.: `Robust H', European Control Conf., 1997.
    6. 6)
      • F.L. Lewis . A survey of linear singular systems. J. Circuits Syst. Signal Process. , 1 , 3 - 36
    7. 7)
      • Sebe, N.: `A new dilated LMI characterization and iterative control system synthesis', 11thIFAC Symp. on Large Scale Systems: Theory and Application, July 2007, Gdansk.
    8. 8)
      • S. Xu , J. Lam . Robust stability and stabilization of discrete singular systems: an equivalent characterization. IEEE Trans. Autom. Control , 568 - 574
    9. 9)
      • P. Apkarian , H.D. Tuan , J. Bernussou . Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations. IEEE Trans. Autom. Control , 1941 - 1946
    10. 10)
      • S. Xu , J. Lam . (2006) Robust control and filtering of singular systems.
    11. 11)
      • Uezato, E., Ikeda, M.: `Strict LMI conditions for stability, robust stabilization, and H', Proc. 38th Conf. on Decision and Control, 1999, Phoenix, USA, p. 4092–4097.
    12. 12)
      • D. Peaucelle , D. Arzelier , O. Bachelier , J. Bernussou . A new robust D-stability condition for real convex polytopic uncertainty. Syst. Control Lett. , 21 - 30
    13. 13)
      • L. Dai . (1989) Singular control systems.
    14. 14)
      • M.C. De Oliveira , J.C. Geromel , J. Bernussou . Extended H2 and H∞ norm characterizations and controller parametrizations for discrete-time systems. Int. J. Control , 666 - 679
    15. 15)
      • Ikeda, M., Lee, T.W., Uezato, E.: `A strict LMI condition for H', IEEE Conf. on Decision and Control, 2000, Sydney, Australia.
    16. 16)
      • Ebihara, Y., Peaucelle, D., Arzelier, D., Hagiwara, T.: `Robust performance analysis of linear time invariant uncertain systems by taking higher-order time derivatives of the state', Proc. 44th IEEE Conf. on Decision and Control, and the European Control Conf., 12–15 December 2005, Seville, Spain.
    17. 17)
      • Y. Ebihara , T. Hagiwara . New dilated LMI characterizations for continuous-time multiobjective controller synthesis. Automatica , 2003 - 2009
    18. 18)
      • H.S. Wang , C.F. Yung , F.R. Chang . (2006) control for nonlinear descriptor systems.
    19. 19)
      • V.J.S. Leite , P.L.D. Peres . An improved LMI condition for robust D-stability of uncertain polytopic systems. IEEE Trans. Autom. Control , 3 , 500 - 504
    20. 20)
      • M.C. Oliveira , R.E. Skelton , S.O. Reza Moheimani . (2001) Stability tests for constrained linear systems, Perspectives in robust control.
    21. 21)
      • M.C. De Oliveira , J. Bernussou , J.C. Geromel . A new discrete-time robust stability condition. Syst. Control Lett. , 261 - 265
    22. 22)
      • I. Masubuchi , Y. Kamitane , A. Ohara , N. Suda . H∞ control for descriptor systems: a matrix inequalities approach. Automatica , 4 , 669 - 673
    23. 23)
      • Sakuwa, R., Fujisaki, Y.: `Robust stability analysis of single-parameter dependent descriptor systems', Proc. 44th IEEE Conf. on Decision and Control, and the European Control Conf., 2005, Spain, p. 2933–2938.
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