Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 878120, 16 pages
http://dx.doi.org/10.1155/2015/878120
Research Article

Robust H-Infinity Stabilization and Resilient Filtering for Discrete-Time Constrained Singular Piecewise-Affine Systems

Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150080, China

Received 7 June 2014; Accepted 12 November 2014

Academic Editor: Asier Ibeas

Copyright © 2015 Zhenhua Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Mirzazad-Barijough and J.-W. Lee, “Stability and transient performance of discrete-time piecewise affine systems,” IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 936–949, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Mirzazad-Barijough and J. W. Lee, “Robust stability and performance analysis of discrete-time piecewise affine systems with disturbances,” in Proceedings of the IEEE 51st Annual Conference on Decision and Control (CDC '12), pp. 4229–4234, 2012.
  3. M. Rubagotti, L. Zaccarian, and A. Bemporad, “Stability analysis of discrete-time piecewise-affine systems over non-invariant domains,” in Proceedings of the 51st IEEE Conference on Decision and Control (CDC '12), pp. 4235–4240, Maui, Hawaii, USA, December 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. N. Eghbal, N. Pariz, and A. Karimpour, “Discontinuous piecewise quadratic Lyapunov functions for planar piecewise affine systems,” Journal of Mathematical Analysis and Applications, vol. 399, no. 2, pp. 586–593, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. M. Rubagotti, S. Trimboli, and A. Bemporad, “Stability and invariance analysis of uncertain discrete-time piecewise affine systems,” IEEE Transactions on Automatic Control, vol. 58, no. 9, pp. 2359–2365, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. Bemporad, G. Ferrari-Trecate, and M. Morari, “Observability and controllability of piecewise affine and hybrid systems,” IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1864–1876, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. W. P. Heemels, M. K. Camlibel, and J. M. Schumacher, “On the dynamic analysis of piecewise-linear networks,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 49, no. 3, pp. 315–327, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. Imura, “Classification and stabilizability analysis of bimodal piecewise affine systems,” International Journal of Robust and Nonlinear Control, vol. 12, no. 10, pp. 897–926, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. Johansson and A. Rantzer, “Computation of piecewise quadratic Lyapunov functions for hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 555–559, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Rantzer and M. Johansson, “Piecewise linear quadratic optimal control,” IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 629–637, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. Johansson, Piecewise Linear Control Systems—A Computational Approach, vol. 284, 2003.
  12. J. Imura and A. van der Schaft, “Characterization of well-posedness of piecewise-linear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 9, pp. 1600–1619, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Feng, “Controller design and analysis of uncertain piecewise-linear systems,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 49, no. 2, pp. 224–232, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Y. Zhu, D. Q. Li, and G. Feng, “H-infinity controller synthesis of uncertain piecewise continuous-time linear systems,” IEE Proceedings-Control Theory and Applications, vol. 152, pp. 513–519, 2005. View at Google Scholar
  15. J. X. Zhang and W. S. Tang, “Output feedback H(infinity) control for uncertain piecewise linear systems,” Journal of Dynamical and Control Systems, vol. 14, no. 1, pp. 121–144, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. Zhang and W. Tang, “Output feedback optimal guaranteed cost control of uncertain piecewise linear systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 5, pp. 569–590, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. G. Bianchini, S. Paoletti, and A. Vicino, “Convex relaxations for L2-gain analysis of piecewise affine/polynomial systems,” International Journal of Control, vol. 86, no. 7, pp. 1207–1213, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. di Bernardo, U. Montanaro, and S. Santini, “Hybrid model reference adaptive control of piecewise affine systems,” IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 304–316, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. W. P. M. H. Heemels, M. Lazar, N. Van De Wouw, and A. Pavlov, “Observer-based control of discrete-time piecewise affine systems: exploiting continuity twice,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 4675–4680, Cancún, Mexico, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Pola and M. D. Di Benedetto, “Symbolic models and control of discrete-time piecewise affine systems: an approximate simulation approach,” IEEE Transactions on Automatic Control, vol. 59, no. 1, pp. 175–180, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. L. Rodrigues and J. P. How, “Observer-based control of piecewise-affine systems,” International Journal of Control, vol. 76, no. 5, pp. 459–477, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. A. Hassibi and S. Boyd, “Quadratic stabilization and control of piecewise-linear systems,” in Proceedings of the American Control Conference (ACC '98), vol. 6, pp. 3659–3664, Philadelphia, Pa, USA, June 1998. View at Publisher · View at Google Scholar · View at Scopus
  23. A. L. Juloski, W. P. Heemels, and S. Weiland, “Observer design for a class of piecewise linear systems,” International Journal of Robust and Nonlinear Control, vol. 17, no. 15, pp. 1387–1404, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. S. Pettersson and B. Lennartson, “Hybrid system stability and robustness verification using linear matrix inequalities,” International Journal of Control, vol. 75, no. 16-17, pp. 1335–1355, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. L. Gao and Y. Wu, “A LMI-based approach for robust stabilization of uncertain linear continuous time singular Markov switched systems with time delays,” in Proceedings of the 25th Chinese Control Conference (CCC '06), pp. 844–849, IEEE, Harbin, China, August 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. G. Zong, Y. Tian, and H. Sun, “Stabilization for a class of piecewise continuous-time switched control systems,” in Proceedings of the IEEE 7th World Congress on Intelligent Control and Automation (WCICA '08), vol. 1–23, pp. 7226–7229, June 2008. View at Publisher · View at Google Scholar
  27. G. Feng, “Observer-based output feedback controller design of piecewise discrete-time linear systems,” IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications, vol. 50, no. 3, pp. 448–451, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. H. Lin and P. J. Antsaklis, “Hybrid state feedback stabilization with l2 performance for disrete-time switched linear systems,” International Journal of Control, vol. 81, no. 7, pp. 1114–1124, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. J. Xu, L. H. Xie, and G. Feng, “Feedback control design for discrete-time piecewise affine systems,” in Proceedings of the International Conference on Control and Automation (ICCA '05), vol. 1, pp. 425–430, IEEE, June 2005. View at Publisher · View at Google Scholar
  30. T. Zhang and G. Feng, “Output tracking of piecewise-linear systems via error feedback regulator with application to synchronization of nonlinear Chua's circuit,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 54, no. 8, pp. 1852–1863, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. Y. L. Wei, M. Wang, and J. B. Qiu, “New approach to delay-dependent H filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions,” IET Control Theory & Applications, vol. 7, no. 5, pp. 684–696, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. P. Shi, E.-K. Boukas, and R. K. Agarwal, “Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters,” IEEE Transactions on Automatic Control, vol. 44, no. 8, pp. 1592–1597, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. C.-H. Lien, J.-D. Chen, C.-T. Lee, R.-S. Chen, and C.-D. Yang, “Robust H filter design for discrete-time switched systems with interval time-varying delay and linear fractional perturbations: LMI optimization approach,” Applied Mathematics and Computation, vol. 219, no. 24, pp. 11395–11407, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. L. Y. Chung, C. H. Lien, K. W. Yu, and J. D. Chen, “Robust H filtering for discrete switched systems with interval time-varying delay,” Signal Processing, vol. 94, no. 1, pp. 661–669, 2014. View at Publisher · View at Google Scholar · View at Scopus
  35. G.-H. Yang and J. L. Wang, “Robust nonfragile Kalman filtering for uncertain linear systems with estimator gain uncertainty,” IEEE Transactions on Automatic Control, vol. 46, no. 2, pp. 343–348, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. G. Song and Z. Wang, “A delay partitioning approach to output feedback control for uncertain discrete time-delay systems with actuator saturation,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 189–202, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. S. Huang, Z. Xiang, and H. R. Karimi, “Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation,” Journal of the Franklin Institute, vol. 350, no. 7, pp. 1865–1885, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. J. Dong and G. H. Yang, “Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties,” IEEE Transactions on Automatic Control, vol. 52, no. 10, pp. 1930–1936, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. B. Zhou, Z. Lin, and G.-R. Duan, “A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems,” Automatica, vol. 45, no. 1, pp. 238–244, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. T. Hu, Z. Lin, and B. M. Chen, “Analysis and design for discrete-time linear systems subject to actuator saturation,” Systems and Control Letters, vol. 45, no. 2, pp. 97–112, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  41. T. Hu, Z. Lin, and B. M. Chen, “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica, vol. 38, no. 2, pp. 351–359, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  42. J. Qiu, T. Zhang, G. Feng, and H. Liu, “Piecewise affine model-based H static output feedback control of constrained non-linear processes,” IET Control Theory & Applications, vol. 4, no. 11, pp. 2315–2330, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  43. Y. Gao, Z. Liu, and H. Chen, “Robust H control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties,” IET Control Theory & Applications, vol. 3, no. 8, pp. 1132–1144, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. Y. Chen, Q. Zhou, and S. Fei, “Robust stabilization and l2-gain control of uncertain discrete-time constrained piecewise-affine systems,” Nonlinear Dynamics, vol. 75, no. 1-2, pp. 127–140, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. K. L. Hsiung and L. Lee, “Lyapunov inequality and bounded real lemma for discrete-time descriptor systems,” IEE Proceedings—Control Theory and Applications, vol. 146, no. 4, pp. 327–331, 1999. View at Publisher · View at Google Scholar · View at Scopus
  46. J. Qiu, G. Feng, and H. Gao, “Approaches to robust H static output feedback control of discrete-time piecewise-affine systems with norm-bounded uncertainties,” International Journal of Robust and Nonlinear Control, vol. 21, no. 7, pp. 790–814, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  47. L. Rodrigues and S. Boyd, “Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization,” Systems & Control Letters, vol. 54, no. 9, pp. 835–853, 2005. View at Publisher · View at Google Scholar · View at Scopus