Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DISTURBANCE ATTENUATION FOR A CLASS OF DISCRETE-TIME SWITCHED SYSTEMS WITH EXPONENTIAL UNCERTAINTY

  • Li, Changlin (College of Computer Science and Information Guizhou University) ;
  • Long, Fei (Institute of Intelligent Information Processing Guizhou University) ;
  • Ren, Guohui (College of Computer Science and Information Guizhou University)
  • Received : 2010.03.04
  • Published : 2011.07.01
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Abstract

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

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References

  1. B. Andrea, M. Pierpaolo, and L. S. Alberto, Controller synthesis on non-uniform and uncertain discrete time domains, Lecture Notes in Comput. Sci. 3414 (2005), 118-133. https://doi.org/10.1007/978-3-540-31954-2_8
  2. P. Gahinet and P. Apkarian, An LMI-based parametrization of all H1 controllers with applications, Proceedings of the 32nd Conference on Decision and Control (1993), 656- 661.
  3. P. Gahinet and P. Apkarian, A linear matrix inequality approach to $H_\infty$ control, Int. J. Robust Nonl. Control 4 (1994), no. 4, 421-448. https://doi.org/10.1002/rnc.4590040403
  4. L. Hetel, J. Daafouz, and C. Iung, Stabilization of arbitrary switched linear systems with unknown time-varying delays, IEEE Trans. Automat. Control 51 (2006), no. 10, 1668-1674. https://doi.org/10.1109/TAC.2006.883030
  5. L. Hetel, J. Daafouz, and C. Iung, LMI control design for a class of exponential uncertain system with applications to network controlled switched systems, Proceedings of the American Control Conference (2007), 1401-1406.
  6. Z. Ji, L. Wang, and D. Xie, Robust $H_\infty$ control and quadratic stabilization of uncertain switched linear systems, Proceedings of the American Control Conference (2004), 4543- 4548.
  7. J. W. Lee and G. E. Dullerud, Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems, SIAM J. Control Optim. 45 (2006), no. 4, 1329-1358. https://doi.org/10.1137/050627538
  8. F. Long and S. M. Fei, Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems, Neurocomputing 71 (2008), no. 7-9, 1741-1747. https://doi.org/10.1016/j.neucom.2007.11.015
  9. F. Long, S. M. Fei, Z. M. Fu, and S. Y. Zheng, Robust $H_\infty$ state feedback control for switched linear systems with linear fractional uncertainties based on LMI, Proceedings of the Chinese Control Conference (2005), 930-934.
  10. F. Long, S. M. Fei, Z. M. Fu, and S. Y. Zheng, Adaptive neural network control for switched system with unknown nonlinear part by using backstepping approach: SISO case, Lecture Notes in Comput. Sci. 3972 (2006), 842-848. https://doi.org/10.1007/11760023_125
  11. F. Long, S. M. Fei, Z. M. Fu, S. Y. Zheng, and W. Wei, $H_\infty$ control and quadratic stabilization of switched linear systems with linear fractional uncertainties via output feedback, Nonlinear Anal. Hybrid Syst. 2 (2008), no. 1, 18-27. https://doi.org/10.1016/j.nahs.2006.11.004
  12. F. Long, C. L. Li, and C. Z. Cui, Robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainty, Journal of Dynamic Systems, Measurement and Control 131 (2009), no. 3, 0345011-0345017.
  13. F. Long, C. L. Li, and C. Z. Cui, Dynamic output feedback $H_\infty$ control for a class of switched linear systems with exponential uncertainty, International Journal of Innovative Computing, Information and Control 6 (2010), no. 4, 1727-1736.
  14. F. Long and W. Wei, On neural network switched stabilization of SISO switched non- linear systems with actuator saturation, Lecture Notes in Comput. Sci. 4491 (2007), 296-305.
  15. H. Nie and J. Zhao, Hybrid state feedback robust $H_\infty$ control for a class of linear sys- tems with time-varying norm-bounded uncertainty, Proceedings of the American Control Conference (2003), 3608-3613.
  16. S. Pettersson and B. Lennartson, Hybrid system stability and robustness veri cation using linear matrix inequalities, Int. J. Control 75 (2005), no. 16-17, 1335-1355.
  17. B. Wittenmark, J. Nilsson, and M. Torngren, Timing problems in real-time control systems, Proceedings of the American Control Conference (1995), 2000-2004.
  18. D. Xie, L. Wang, F. Hao, and G. Xie, LMI approach to $L_2$-gain analysis and control synthesis of uncertain switched systems, IEE Proc. Control Theory Application 151 (2004), no. 1, 21-28. https://doi.org/10.1049/ip-cta:20040010
  19. S. Yang, Z. G. Xiang, Q. W. Chen, and W. L. Hu, Control of switched systems with actuator saturation, J. Control Theory Appl. 1 (2006), 38-43.
  20. G. Zhai, H. Lin, and P. J. Antsaklis, Quadratic stabilizability of switched linear systems with polytopic uncertainties, Int. J. Control 76 (2003), no. 7, 747-753. https://doi.org/10.1080/0020717031000114968
  21. W. Zhang, M. S. Branicky, and S. M. Phillips, Stability of networked control systems, IEEE Control Syst. Mag. 21 (2001), no. 1, 84-99. https://doi.org/10.1109/37.898794