We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 November 2024
Reseach Article

Uncertain 2D Continuous Systems with State Delay: Filter Design using an Polynomial Approach

by C.El-Kasri, A. Hmamed, E.H. Tissir, F. Tadeo
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 44 - Number 18
Year of Publication: 2012
Authors: C.El-Kasri, A. Hmamed, E.H. Tissir, F. Tadeo
10.5120/6362-7604

C.El-Kasri, A. Hmamed, E.H. Tissir, F. Tadeo . Uncertain 2D Continuous Systems with State Delay: Filter Design using an Polynomial Approach. International Journal of Computer Applications. 44, 18 ( April 2012), 13-21. DOI=10.5120/6362-7604

@article{ 10.5120/6362-7604,
author = { C.El-Kasri, A. Hmamed, E.H. Tissir, F. Tadeo },
title = { Uncertain 2D Continuous Systems with State Delay: Filter Design using an Polynomial Approach },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 44 },
number = { 18 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 13-21 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume44/number18/6362-7604/ },
doi = { 10.5120/6362-7604 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:35:51.975094+05:30
%A C.El-Kasri
%A A. Hmamed
%A E.H. Tissir
%A F. Tadeo
%T Uncertain 2D Continuous Systems with State Delay: Filter Design using an Polynomial Approach
%J International Journal of Computer Applications
%@ 0975-8887
%V 44
%N 18
%P 13-21
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper proposes a methodology to design filters that extract information from noisy signals. From a mathematical point of view, a method is used based on homogeneous polynomially parameter-dependent (HPPD) matrices of arbitrary degree. The optimal filter is then obtained by solving a convex optimization problem using off-the-self software. To show the effectiveness of the proposed filter design methodology some examples are solved, and the solution is illustrated using computer simulations.

References
  1. M. Allouche, M. Souissi, M. Chaabane, D. Mehdi and F. Tadeo, "Takagi-Sugeno Fuzzy Observer Design for Induction Motors with Immeasurable Decision Variables: State Estimation and Sensor Fault Detection," International Journal of Computer Applications, vol. 23 No. 4, pp. 44-51, 2011.
  2. A. A. Babu, R. Yellasiri and N. and P. Hegde. "Robust Speech Processing in EW Environment. " International Journal of Computer Applications, vol. 38, No. 11, pp. 46-50, 2012.
  3. A. Mehrotra, K. K. Singh and M. J. Nigam, "A Novel Algorithm for Impulse Noise Removal and Edge Detection," International Journal of Computer Applications, vol. 38, No. 7, pp. 30-34, 2012.
  4. R. N. Banavar and J. L. Speyer, "A linear-quadratic game approach to estimation and smoothing," in Proc. 1991 American Control Conference, Boston, MA, June 1991, pp. 2818-2822.
  5. M. Chau, A. Luo and V. Chau. "PID-Fuzzy Control Method with Time Delay Compensation for Hybrid Active Power Filter with Injection Circuit," International Journal of Computer Applications, vol. 36, no. 7, pp. 15-21, 2011.
  6. F. F. G. Areed, M. S. El-Kasassy and Kh. A. Mahmoud, "Design of Neuro-Fuzzy Controller for a Rotary Dryer," International Journal of Computer Applications, vol. 37, no. 5, pp. 34-41, 2012.
  7. C. El-Kasri, A. Hmamed, T. Alvarez and F. Tadeo, "Robust Filtering of 2D Roesser Discrete Systems : A Polynomial Approach," Mathematical Problems in Engineering, vol. 2012, pp. 1-15, 2012.
  8. C. W. Chen, J. S. H. Tsai, and L. S. Shieh, "Modeling and solution of two-dimensional input time-delay system," J. Franklin Inst. , vol. 337, pp. 569-578, 2002.
  9. C. E. De Sousa, L. Xie and Y. Wang, " filtering for a class of uncertain nonlinear systems," Systems and Control Letters, vol. 20, pp. 419 - 426, 1993.
  10. C. Du and L. Xie, " Cntrol and Filtering of two-Dimensional Systems," Heidelberg, Germany, Springer Verlag, 2002.
  11. M. Fu, "Interpolation approach to optimal estimation and its interconnection to loop transfer recovery," Systems and Control Letters, vol. 17, pp. 29 - 36, 1991.
  12. K. Galkowski, "LMI based stability analysis for 2D continuous systems," in Proc. 9th IEEE int. Conf. Electron. , Circuits Syst. , Dubrovnik, Croatia, pp. 923-926, Sep. 2002.
  13. H. Gao and C. Wang "A delay-dependent approach to robust H filtering for uncertain discrete-time state-delayed systems," IEEE Trans. Signal Process. , vol. 52, no. 6, pp. 1631-1640, Jun. 2004.
  14. H. Gao and C. Wang, "Robust filtering for uncertain systems with multiple time-varying state delays," IEEE Trans. Circuits Syst. I, vol. 50, no. 4, pp. 594-599, Apr. 2003.
  15. E. Gershon, D. J. N. Limebeer, U. Shaked and I. Yaesh, "Robust filtering of stationery continuous-times linear systems with stochastic uncertainties", IEEE Trans. automat. Control, Vol. 46, pp. 1788 - 1793, 2001.
  16. A. Hmamed, M. Alfidi, A. Benzaouia, and F. Tadeo, "LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems", Mathematical Problems in Engineering, Article ID 356124, 11 pages, 2008.
  17. A. Hmamed, M. Alfidi, A. Benzaouia, and F. Tadeo, "Robust stabilization under linear fractional parametric uncertainties of two-Dimensional system wiyh Roesser models," Int. J. of Sciences and Techniques of Automatic Control and Computer Engineering, Special Issue, pp. 336-348, Dec 2007.
  18. C. El-Kasri, A. Hmamed, T. Alvarez, F. Tadeo, "Robust filtering for uncertain 2-D continuous systems, based on a polynomially parameter-dependent Lyapunov function," 7th International Workshop on Multidimensional (nD) Systems (nDs), Sept. 2011.
  19. A. Hmamed, F. Mesquine, F. Tadeo, M. Benhayoun and A. Benzaouia,"Stabilization of 2D saturated systems by state feedback control," Multidim Syst and Sign Process, vol. 21, no. 3, pp. 277-292, Apr 2010.
  20. J. Huang, G. Lu, and X. Zou, "Existence of traveling wave fronts of delayed lattice differential equations," J. Math. Anal. Appl. , vol. 298, pp. 538-558, 2004.
  21. S. H. Jiu and J. B. Park, "Robust filtering for polytopic uncertain systems via convex optimization," Proc. Inst. Elect. Eng. Control Theory Appl, vol. 148, pp: 55 - 59, 2001.
  22. M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems. New York : Marcel Dekker, 2000.
  23. N. E. Mastorakis and M. Swamy, "A new method for computing the stability margin of two dimensional continuous systems," IEEE Trans. Circuits and Systems I, vol. 49, pp. 869 - 872, 2002.
  24. K. M. Nagpal, P. P. Khargonekov, "Filtering and smoothing in an setting", IEEE Trans. Automat. Control, vol. 36, pp. 152 - 166, 1991.
  25. R. C. L. F. Oliveira, P. L. D. Peres. LMI Conditions for Robust Stability Analysis Based on Polynomially Parameter dependent Lyapunov Functions. Systems and Control Letters, vol. 55, no. 1, pp. 52-61, 2006.
  26. R. M. Palhares, C. E. D. Souza, and P. L. D. Peres, "Robust H filtering for uncertain discrete-time state-delayed systems," IEEE Trans. Signal Process. , vol. 49, no. 8, pp. 1696-1703, Aug. 2001.
  27. P. G. Park, T. Keileth, " via convex optimization", Int. J. Control, vol. 66, pp. 15 - 22, 1997.
  28. W. Paszke, J. Lam, K. Galkowski, S. Xu, and Z. Lin, "Robust stability and stabilization of 2-D discrete state-delayed systems," Syst. Control Lett. , vol. 51, pp. 277-291, 2004.
  29. W. Paszke, J. Lam, K. Galkowski, S. Xu, and E. Rogers, " control of 2-D linear state-delayed systems," presented at the 4th IFAC Workshop Time-Delay Systems, Rocquencourt, France, Sep. 8-10, 2003.
  30. M. S. Pickarski, "Algebraic characterization of matrices whose multivariable characteristic polynomial is Hermitian", in Proc. Int. Symp. Operator Theory, Lubbock, TX, 1977, pp. 126-126.
  31. E. Rogers, K. Galkowski, and D. H. Owens, "Delay differential control theory applied to differential linear repetitive processes," presented at the Amer. Control Conf. , Anchorage, AK, May 2002.
  32. U. Shaked, " minimum error state estimation of linear stationary processes", IEEE Trans. Aut. Control, vol. 35, pp: 554 - 558, 1990.
  33. H. D. Tuan, P. Apkarian, T. Q. Nguyen and T. Narikiys, "Robust mixed filtering of 2-D systems", IEEE Trans. Singal Process, vol. 50, pp. 1759 - 1771, 2002.
  34. L. Xie, C. Du, C. Zhang and Y. C. Soh, " deconvolution filtering of 2-D digital systems", IEEE Trans. Signal Process, vol. 50, pp : 2319 - 2332, 2003.
  35. S. Xu,J. Lam,Y. Zou, Z. Lin, and W. Paszke, "Robust Filtering for Uncertain 2-D Continuous Systems" IEEE Transactions on Signal Processing, vol. 53, pp. 1731-1738, 2005.
  36. S. Xu and P. Van Dooren, "Robust filtering for a class of nonlinear systems with state delay and parameter uncertainty", Int. J. Control, vol. 75, pp. 766 - 774, 2002.
  37. I. Yaesh and U. Shaked, "Game theory approach to optimal linear state estimation and its relation to the minimum -norm estimation", IEEE Trans. Automat. Control, vol. 37, pp. 828 - 831, 1992.
  38. I. Yaesh and U. Shaked, "Game theory approach to optimal linear estimation in the minimum norm sense," in Proc. 28th IEEE Conf. Decision Control, Tampa, FL, Dec. 1989, pp. 421-425.
  39. B. G. Zhang and C. J. Tian, "Oscillation criteria of a class of partial difference equations with delays," Comput. Math. with Appl. , vol. 48, pp. 291-303, 2004.
  40. B. G. Zhang and C. J. Tian, "Stability criteria for a class of linear delay partial difference equations," Comput. Math. with Appl. , vol. 38, pp. 37-43, 1999.
Index Terms

Computer Science
Information Sciences

Keywords

Systems Theory Uncertainty Delays Filtering Linear Matrix Inequalities (lmi)