Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 159745, 6 pages
http://dx.doi.org/10.1155/2014/159745
Research Article

Robust Stability Criteria of Roesser-Type Discrete-Time Two-Dimensional Systems with Parameter Uncertainties

1School of Renewable Energy, Shenyang Institute of Engineering, Shenyang, Liaoning 110136, China
2School of Engineering and Information Technology, Murdoch University, Perth, WA 6150, Australia

Received 9 January 2014; Accepted 2 February 2014; Published 16 March 2014

Academic Editor: Ming Liu

Copyright © 2014 Yan Zhao 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. D. Henrion, D. Arzelier, D. Peaucelle, and M. Šebek, “An LMI condition for robust stability of polynomial matrix polytopes,” Automatica, vol. 37, no. 3, pp. 461–468, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Yin, H. Luo, and S. Ding, “Real-time implementation of fault-tolerant control systems with performance optimization,” IEEE Transactions on Industrial Electronics, vol. 64, no. 5, pp. 2402–2411, 2014. View at Google Scholar
  3. S. Yin, S. X. Ding, A. H. A. Sari, and H. Hao, “Data-driven monitoring for stochastic systems and its application on batch process,” International Journal of Systems Science, vol. 44, no. 7, pp. 1366–1376, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Yin, S. Ding, A. Haghani, H. Hao, and P. Zhang, “A comparison study of basic datadriven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process,” Journal of Process Control, vol. 22, no. 9, pp. 1567–1581, 2012. View at Google Scholar
  5. D. Henrion, D. Arzelier, and D. Peaucelle, “Positive polynomial matrices and improved LMI robustness conditions,” Automatica, vol. 39, no. 8, pp. 1479–1485, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. L. D. Peres and J. C. Geromel, “2 control for discrete-time systems optimality and robustness,” Automatica, vol. 29, no. 1, pp. 225–228, 1993. View at Publisher · View at Google Scholar · View at Scopus
  7. P. L. D. Peres, J. C. Geromel, and J. Bernussou, “Quadratic stabilizability of linear uncertain systems in convex-bounded domains,” Automatica, vol. 29, no. 2, pp. 491–493, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Gahinet, P. Apkarian, and M. Chilali, “Affine parameter-dependent Lyapunov functions and real parametric uncertainty,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 436–442, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. Fornasini and G. Marchesini, “State–space realization theory of two–dimensional filters,” IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 484–492, 1976. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Transactions on Automatic Control, vol. 20, pp. 1–10, 1975. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. H. Owens, N. Amann, E. Rogers, and M. French, “Analysis of linear iterative learning control schemes: a 2D systems/repetitive processes approach,” Multidimensional Systems and Signal Processing, vol. 11, no. 1-2, pp. 125–177, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. B. Sulikowski, K. Gałkowski, E. Rogers, and D. H. Owens, “Output feedback control of discrete linear repetitive processes,” Automatica, vol. 40, no. 12, pp. 2167–2173, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Sulikowski, K. Galkowski, E. Rogers, and D. H. Owens, “PI control of discrete linear repetitive processes,” Automatica, vol. 42, no. 5, pp. 877–880, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Yin, G. Wang, and H. Karimi, “Data-driven design of robust fault detection system for wind turbines, Mechatronics,” 2013. View at Publisher · View at Google Scholar
  15. V. Singh, “Elimination of overflow oscillations in 2-D digital filters employing saturation arithmetic: an LMI approach,” IEEE Signal Processing Letters, vol. 12, no. 3, pp. 246–249, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. 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
  17. A. Dhawan and H. Kar, “Optimal guaranteed cost control of 2-D discrete uncertain systems: an LMI approach,” Signal Processing, vol. 87, no. 12, pp. 3075–3085, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. V. Singh, “New LMI condition for the nonexistence of overflow oscillations in 2-D state-space digital filters using saturation arithmetic,” Digital Signal Processing, vol. 17, no. 1, pp. 345–352, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. V. Singh, “Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using two's complement arithmetic,” Digital Signal Processing, vol. 22, no. 3, pp. 471–475, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. V. Singh, “On global asymptotic stability of 2-D discrete systems with state saturation,” Physics Letters A, vol. 372, no. 32, pp. 5287–5289, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. Dhawan and H. Kar, “An LMI approach to robust optimal guaranteed cost control of 2-D discrete systems described by the Roesser model,” Signal Processing, vol. 90, no. 9, pp. 2648–2654, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Dey and H. Kar, “Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: an LMI approach,” Digital Signal Processing, vol. 21, no. 2, pp. 262–269, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Dhawan and H. Kar, “An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems,” Signal Processing, vol. 91, no. 4, pp. 1032–1035, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. V. Singh, “New approach to stability of 2-D discrete systems with state saturation,” Signal Processing, vol. 92, no. 1, pp. 240–247, 2012. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Kar, “A new criterion for the global asymptotic stability of 2-D state-space digital filters with twos complement overflow arithmetic,” Signal Processing, vol. 92, no. 9, pp. 2322–2326, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. A. Dey and H. Kar, “An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities,” Digital Signal Processing, vol. 22, no. 4, pp. 633–639, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  27. W. Sun, H. Gao Sr., and O. Kaynak, “Finite frequency control for vehicle active suspension systems,” IEEE Transactions on Control Systems Technology, vol. 19, no. 2, pp. 416–422, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. W. Sun, Y. Zhao, J. Li, L. Zhang, and H. Gao, “Active suspension control with frequency band constraints and actuator input delay,” IEEE Transactions on Industrial Electronics, vol. 59, no. 1, pp. 530–537, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. Suzuki, S. Morioka, and H. Ueda, “Cooking support with information projection over ingredient,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 12, pp. 4753–4763, 2013. View at Google Scholar
  30. M. Nakatani and T. Ohno, “An integrated model depicting psychology of active/Non-active internet users: how to motivate people to use internet at home,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 12, pp. 4765–4779, 2013. View at Google Scholar