MODEL REDUCTION FOR DISCRETE-TIME SWITCHED LINEAR TIME-DELAY SYSTEMS VIA THE H∞ ROBUST STABILITY

Abderazik Birouche, Benjamin Mourllion, and Michel Basset

References

  1. [1] A.C. Antoulas, Lectures on the approximation of large-scaledynamical systems (Philadelphia, PA: Society for Industrialand Applied Mathematics SIAM, 2005).
  2. [2] B. Moore, Principal component analysis in linear systems: Con-trollability, observability, and model reduction. IEEE Trans-actions Automatic Control, 26 (1), 1981, 17–32.
  3. [3] J. Lam, H. Gao, S. Xu, & C. Wang, h∞ and l∞, l2 modelreduction for system input with sector nonlinearities. Journal ofOptimization Theory and Applications, 125 (1), 2005, 137–155.
  4. [4] W.-Y. Yan & J. Lam, An approximate approach to h2 optimalmodel reduction. IEEE Transactions on Automatic Control,44 (7), 1999, 1341–1358.
  5. [5] S. Boyd, L.E. Ghaoui, B. Feron, & V. Balakrishnan, Linearmatrix inequalities in system and control theory (Philadelphia,PA: Studies in Applied Mathematics, 1994).
  6. [6] K.M. Grigoriadis, Optimal h∞ model reduction via linear ma-trix inequalities: Continuous- and discrete-time cases. Systemsand Control Letters, 26, 1995, 321–333.
  7. [7] P. Shi, Z. Lin, & Y. Shi, Robust output feedback control fordiscrete time-delay uncertain systems. Control and IntelligentSystems, 34 (1), 2006, 57–63.
  8. [8] C.Y. Lu, J.S.H. Tsai, & T.J. Su, Delay-dependent robust h∞filtering for interval systems with state delays. Control andIntelligent Systems, 34 (2), 2006, 113–118.
  9. [9] D. Liberzon, Switching in systems and control. (Boston:Birkh¨auser, 2003).
  10. [10] A. Bemporad, G. Ferrari-Trecate, & M. Morari, Observabilityand controllability of piecewise affine and hybrid systems. IEEETransactions Automatic Control, 45 (10), 2000, 1864–1876.
  11. [11] M. Johansson, Piecewise linear control systems Lecture notesin control and information sciences, Germany, 2003.
  12. [12] G. Huijun, L. James, & W. Changhong, Model simplificationfor switched hybrid systems. Systems and Control Letters,55 (12), 2006, 1015–1021.
  13. [13] L. Wu, P. Shi, H. Gao, & C. Wang, h∞ mode reduction for two-dimensional discrete state-delayed systems. IEEE Proceedingsof Vision, Image and Signal Processing, 153 (6), 2006, 769–784.
  14. [14] L. Zhang, P. Shi, E.K. Boukas, & C. Wang, h∞ modelreduction for uncertain switched linear discrete-time systems.Automatica, 44 (11), 2008, 2944–2949.
  15. [15] L. Wu, D.W.C. Ho, & J. Lam, h∞ model reduction forcontinuous-time switched stochastic hybrid systems. Interna-tional Journal of Systems Science, 40, 2009, 1241–1251.
  16. [16] X. Dongmei, X. Ning, & C. Xiaoxin, Lmi approach to h2reduction model of switched systems, Proc. 7th World Congresson Intelligent Control and Automation WCICA 2008, 25–27June 2008, 6381–6386.
  17. [17] X. Dongmei, W. Yongjun, & C. Xiaoxin, Stabilization ofdiscrete-time switched systems with input time delay and itsapplications in networked control systems. Circuits, Systems,and Signal Processing, 28 (4), 2009, 595–1607.
  18. [18] Y. Zhang, G. Duan, & X. Zhang, h∞-performance analysis fordiscrete-time switched systems with time-delay. Proc. IEEE85Int. Conf. Automation and Logistics ICAL 2008, 2008, 1698–1702.
  19. [19] Z. Wen-An & Y. Li, Stability analysis for discrete-time switchedtime-delay systems. Automatica, 45 (10), 2009, 2265–2271.
  20. [20] D. Du, B. Jiang, P. Shi, & S. Zhou, h∞ filtering of discrete-time switched systems with state delays via switched Lyapunovfunction approach. IEEE Transactions on Automatic Control,52 (8), 2007, 1520–1525.
  21. [21] D. Wang, W. Wang, & P. Shi, Correction to h∞ filtering ofdiscrete-time switched systems with state delays via switchedLyapunov function approach. IEEE Transactions on AutomaticControl, 54 (6), 2009, 1428–1429.
  22. [22] J. Daafouz & J. Bernussou, Parameter dependent Lyapunovfunctions for discrete time systems with time varying paramet-ric uncertainties. Systems Control Letters, 43, 2001, 355–359.

Important Links:

Go Back