Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 748930, 8 pages
http://dx.doi.org/10.1155/2014/748930
Research Article

Robust Simultaneous Stabilization Control Method for Two Port-Controlled Hamiltonian Systems: Controller Parameterization

1School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2School of Computer Science and Educational Software, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 19 March 2014; Accepted 15 July 2014; Published 5 August 2014

Academic Editor: Fabio M. Camilli

Copyright © 2014 Zhong Cao and Xiaorong Hou. 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. B. Maschke, R. Ortega, and A. J. van der Schaft, “Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation,” IEEE Transactions on Automatic Control, vol. 45, no. 8, pp. 1498–1502, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. Z. Xi and D. Cheng, “Passivity-based stabilization and H control of the Hamiltonian control systems with dissipation and its applications to power systems,” International Journal of Control, vol. 73, no. 18, pp. 1686–1691, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. Ortega, A. van der Schaft, B. Maschke, and G. Escobar, “Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems,” Automatica, vol. 38, no. 4, pp. 585–596, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Fujimoto, K. Sakurama, and T. Sugie, “Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations,” Automatica, vol. 39, no. 12, pp. 2059–2069, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. J. van der Schaft, “Port-controlled Hamiltonian systems: towards a theory for control and design of nonlinear physical systems,” Journal of the Society of Instrument and Control Engineers of Japan, vol. 39, no. 2, pp. 91–98, 2000. View at Google Scholar
  6. R. Ortega, A. van der Schaft, F. Castaños, and A. Astolfi, “Control by interconnection and standard passivity-based control of port-Hamiltonian systems,” IEEE Transactions on Automatic Control, vol. 53, no. 11, pp. 2527–2542, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. D. Cheng, Z. Xi, Y. Hong, and H. Qin, “Energy-based stabilization of forced hamiltonian systems and its application to power systems,” Control Theory and Applications, vol. 17, no. 6, pp. 798–802, 2000. View at Google Scholar · View at Scopus
  8. X. Xin and M. Kaneda, “New analytical results of the energy based swinging up control of the acrobot,” in Proceedings of the 43rd IEEE Conference on Decision and Control (CDC '04), vol. 1, pp. 704–709, December 2004. View at Scopus
  9. X. Xin and M. Kaneda, “Analysis of the energy-based swing-up control of the Acrobot,” International Journal of Robust and Nonlinear Control, vol. 17, no. 16, pp. 1503–1524, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. P. T. Kabamba and C. Yang, “Simultaneous controller design for linear time-invariant systems,” IEEE Transactions on Automatic Control, vol. 36, no. 1, pp. 106–111, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. R. Broussard and C. S. McLean, “An algorithm for simultaneous stabilization using decentralized constant gain output feedback,” IEEE Transactions on Automatic Control, vol. 38, no. 3, pp. 450–455, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Cao, Y. Sun, and J. Lam, “Simultaneous stabilization via static output feedback and state feedback,” IEEE Transactions on Automatic Control, vol. 44, no. 6, pp. 1277–1282, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. S. M. Karbassi and H. A. Tehrani, “Parameterizations of the state feedback controllers for linear multivariable systems,” Computers and Mathematics with Applications, vol. 44, no. 8-9, pp. 1057–1065, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. F. Saadatjoo, V. Derhami, and S. M. Karbassi, “Simultaneous control of linear systems by state feedback,” Computers & Mathematics with Applications, vol. 58, no. 1, pp. 154–160, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. B. Ho-Mock-Qai and W. P. Dayawansa, “Simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback,” SIAM Journal on Control and Optimization, vol. 37, no. 6, pp. 1701–1725, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Y. Wang, G. Feng, and D. Cheng, “Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems,” Automatica, vol. 43, no. 3, pp. 403–415, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. J. Xu, L. Xie, and Y. Wang, “Simultaneous stabilization and robust control of polynomial nonlinear systems using SOS techniques,” IEEE Transactions on Automatic Control, vol. 54, no. 8, pp. 1892–1897, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. L. Sun and Y. Wang, “Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method,” Science in China F: Information Sciences, vol. 52, no. 11, pp. 2140–2152, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. Wei, Y. Wang, and X. Hu, “Parallel simultaneous stabilization of a set of port-controlled Hamiltonian systems subject to actuator saturation,” Journal of Systems Science and Complexity, vol. 24, no. 1, pp. 120–139, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. Y. L. Abdel-Magid, M. A. Abido, S. Al-Baiyat, and A. H. Mantawy, “Simultaneous stabilization of multimachine power systems via genetic algorithms,” IEEE Transactions on Power Systems, vol. 14, no. 4, pp. 1428–1439, 1999. View at Publisher · View at Google Scholar · View at Scopus
  21. W. M. Lu and J. C. Doyle, “H control of nonlinear systems via output feedback: controller parameterization,” IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2517–2521, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. A. Isidori and A. Astolfi, “Disturbance attenuation and H-control via measurement feedback in nonlinear systems,” IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1283–1293, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. A. Astolfi, “Parameterization of output feedback controller that satisfy an H norm bound,” in Proceedings of the 2nd European Control Conference, pp. 74–78, Groningen, The Netherlands, 1993.
  24. C. F. Yung, J. L. Wu, and T. T. Lee, “Parameterization of nonlinear H state-feedback controllers,” Automatica, vol. 33, no. 8, pp. 1587–1590, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. S. Xu and X. Hou, “A family of H controllers for dissipative Hamiltonian systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 11, pp. 1258–1269, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. S. Xu and X. Hou, “A family of adaptive H controllers with full information for dissipative Hamiltonian systems,” International Journal of Automation and Computing, vol. 8, no. 2, pp. 209–214, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. A. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, vol. 218 of Lecture Notes in Control and Information Sciences, Springer, Berlin , Germany, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Y. Wang, D. Cheng, C. Li, and Y. Ge, “Dissipative Hamiltonian realization and energy-based L2-disturbance attenuation control of multimachine power systems,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1428–1433, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Y. Wang, D. Cheng, and S. S. Ge, “Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions,” Systems and Control Letters, vol. 56, no. 2, pp. 141–149, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  30. B. F. Caviness and J. R. Johnson, Quantifier Elimination and Cylindrical Algebraic Decomposition, Springer, New York, NY, USA, 1998.
  31. K. N. Swamy, “On Sylvesters criterion for positive- semidefinite matrices,” IEEE Transactions on Automatic Control, vol. 18, no. 3, 306 pages, 1973. View at Google Scholar · View at Scopus