Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 847178, 9 pages
http://dx.doi.org/10.5402/2012/847178
Research Article

Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation

1Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad 211004, India
2Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology, Allahabad 211004, India

Received 7 November 2011; Accepted 3 December 2011

Academic Editors: J. Buick, P. B. Vasconcelos, and Q.-W. Wang

Copyright © 2012 Richa Negi 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. N. Kapoor, A. R. Teel, and P. Daoutidis, “An anti-windup design for linear systems with input saturation,” Automatica, vol. 34, no. 5, pp. 559–574, 1998. View at Google Scholar · View at Scopus
  2. Y. Y. Cao, Z. Lin, and D. G. Ward, “An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation,” IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 140–145, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. G. Grimm, A. R. Teel, and L. Zaccarian, “The l2 anti-windup problem for discrete-time linear systems: definition and solutions,” Systems and Control Letters, vol. 57, no. 4, pp. 356–364, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. P. C. Chen and J. S. Shamma, “Gain-scheduled 1-optimal control for boiler-turbine dynamics with actuator saturation,” Journal of Process Control, vol. 14, no. 3, pp. 263–277, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. M. V. Kothare and M. Morari, “Multiplier theory for stability analysis of anti-windup control systems,” Automatica, vol. 35, no. 5, pp. 917–928, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. T. Hu, A. R. Teel, and L. Zaccarian, “Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions,” IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1770–1786, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. M. Gomes Da Silva Jr. and S. Tarbouriech, “Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach,” IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 119–125, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. S. Shamma, “Anti-windup via constrained regulation with observers,” in Proceedings of the American Control Conference (ACC '99), pp. 2481–2485, San Diego, Calif, USA, June 1999. View at Scopus
  9. J. M. Gomes Da Silva Jr. and S. Tarbouriech, “Anti-windup design with guaranteed regions of stability for discrete-time linear systems,” Systems and Control Letters, vol. 55, no. 3, pp. 184–192, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. M. Gomes da Silva Jr. and S. Tarbouriech, “Antiwindup design with guaranteed regions of stability: an LMI-based approach,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 106–111, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. L. L. Giovanini, “Model predictive control with amplitude and rate actuator saturation,” ISA Transactions, vol. 42, no. 2, pp. 227–240, 2003. View at Google Scholar · View at Scopus
  12. M. Zhang and C. Jiang, “Problem and its solution for actuator saturation of integrating process with dead time,” ISA Transactions, vol. 47, no. 1, pp. 80–84, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  13. C. Roos, J. M. Biannic, S. Tarbouriech, C. Prieur, and M. Jeanneau, “On-ground aircraft control design using a parameter-varying anti-windup approach,” Aerospace Science and Technology, vol. 14, no. 7, pp. 459–471, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. L. Zaccarian, Y. Li, E. Weyer, M. Cantoni, and A. R. Teel, “Anti-windup for marginally stable plants and its application to open water channel control systems,” Control Engineering Practice, vol. 15, no. 2, pp. 261–272, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. T. S. Kwon and S. K. Sul, “Novel antiwindup of a current regulator of a surface-mounted permanent-magnet motor for flux-weakening control,” IEEE Transactions on Industry Applications, vol. 42, no. 5, pp. 1293–1300, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. H. A. Fertik and C. W. Ross, “Direct digital control algorithm with anti-windup feature,” ISA Transactions, vol. 6, pp. 317–328, 1967. View at Google Scholar
  17. K. S. Walgama and J. Sternby, “Conditioning technique for multiinput multioutput processes with input saturation,” IEE Proceedings D, vol. 140, no. 4, pp. 231–241, 1993. View at Google Scholar · View at Scopus
  18. S. Tarbouriech and M. Turner, “Anti-windup design: an overview of some recent advances and open problems,” IET Control Theory and Applications, vol. 3, no. 1, pp. 1–19, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. E. Fornasini and G. Marchesini, “Doubly-indexed dynamical systems: state-space models and structural properties,” Mathematical Systems Theory, vol. 12, no. 1, pp. 59–72, 1978. View at Publisher · View at Google Scholar · View at Scopus
  20. T. Kaczorek, Two-Dimensional Linear Systems, Springer, Berlin, Germany, 1985.
  21. R. N. Bracewell, Two-Dimensional Imaging, Prentice-Hall Signal Processing Series, Prentice Hall, Englewood Cliffs, NJ, USA, 1995.
  22. N. K. Bose, Applied Multidimensional System Theory, Van Nostrand Reinhold, New York, NY, USA, 1982.
  23. T. Hinamoto, “2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 2, pp. 102–109, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. T. Hinamoto, “Stability of 2-D discrete systems described by the fornasini-marchesini second model,” IEEE Transactions on Circuits and Systems I, vol. 44, no. 3, pp. 254–257, 1997. View at Google Scholar · View at Scopus
  25. W. S. Lu, “On a Lyapunov approach to stability analysis of 2-D digital filters,” IEEE Transactions on Circuits and Systems I, vol. 41, no. 10, pp. 665–669, 1994. View at Publisher · View at Google Scholar · View at Scopus
  26. T. Ooba, “On stability analysis of 2-D systems based on 2-D Lyapunov matrix inequalities,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 8, pp. 1263–1265, 2000. View at Publisher · View at Google Scholar · View at Scopus
  27. D. Liu, “Lyapunov stability of two-dimensional digital filters with overflow nonlinearities,” IEEE Transactions on Circuits and Systems I, vol. 45, no. 5, pp. 574–577, 1998. View at Google Scholar · View at Scopus
  28. H. Kar and V. Singh, “An improved criterion for the asymptotic stability of 2-D digital filters described by the fornasini-marchesini second model using saturation arithmetic,” IEEE Transactions on Circuits and Systems I, vol. 46, no. 11, pp. 1412–1413, 1999. View at Google Scholar · View at Scopus
  29. H. Kar and V. Singh, “Stability analysis of 2-D digital filters described by the Fornasini-Marchesini second model using overflow nonlinearities,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 5, pp. 612–617, 2001. View at Publisher · View at Google Scholar · View at Scopus
  30. H. Kar and V. Singh, “Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities,” IEEE Transactions on Signal Processing, vol. 49, no. 5, pp. 1097–1105, 2001. View at Publisher · View at Google Scholar · View at Scopus
  31. V. Singh, “Stability analysis of 2-D discrete systems described by the Fornasini-Marchesini second model with state saturation,” IEEE Transactions on Circuits and Systems II, vol. 55, no. 8, pp. 793–796, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. H. Kar and V. Singh, “Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities,” IEEE Transactions on Circuits and Systems II, vol. 51, no. 11, pp. 598–602, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. V. Singh, “Robust stability of 2-D digital filters employing saturation,” IEEE Signal Processing Letters, vol. 12, no. 2, pp. 142–145, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Hmamed, F. Mesquine, F. Tadeo, M. Benhayoun, and A. Benzaouia, “Stabilization of 2D saturated systems by state feedback control,” Multidimensional Systems and Signal Processing, vol. 21, no. 3, pp. 277–292, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  35. S. Boyd, L. EI-Ghaousi, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
  36. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox-For Use with MATLAB, MathWorks, Inc., Natic, Mass, USA, 1995.
  37. W. Marszalek, “Two-dimensional state-space discrete models for hyperbolic partial differential equations,” Applied Mathematical Modelling, vol. 8, no. 1, pp. 11–14, 1984. View at Google Scholar · View at Scopus
  38. C. Du, L. Xie, and C. Zhang, “H∞ control and robust stabilization of two-dimensional systems in Roesser models,” Automatica, vol. 37, no. 2, pp. 205–211, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  39. J. S. H. Tsai, J. S. Li, and L. S. Shieh, “Discretized quadratic optimal control for continuous-time two-dimensional systems,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 1, pp. 116–125, 2002. View at Publisher · View at Google Scholar · View at Scopus