A Comparison Between Famous Discrete State Space Models

References

[1] T. Kaczorek, Two-Dimensional Linear Systems, Springer, Berlin, 1985.

[2] Derek Rowell” State-Space Representation of LTI Systems” 2.14 Analysis and Design of Feedback Control Systems.

[3] Attasi in “Systemes lineaires homogenes a deux indices,” IRIA Rapport Laboria, No.

[4] S. Y. Kung, B. Levy, M. Morf, T. Kailath, "New results in 2-d systems theory part ii: 2-d state-space models; realization and the notions of controllability’ observability and minimality", Proceedings of the IEEE, vol. 65, no. 6, pp. 945-961, June 1977.

[5] E. Fornasini, G. Marchesini, “Doubly indexed dynamical systems: Statespace models and structural properties,” Math. Syst. Theory, vol. 12, pp.59-72, 1978.

[6] Prashant k shah,’ LMI based Stability criteria for 2-D PSV system described by FM-2 Model,submitted

[7] Prashant k shah,’Stability analysis of 2-D PSV system represented by Givone–Roesser Model’,submitted

[8] Dr.(Mrs.) U. D. Dalal, Dr. S. N. sharma & Prof. Prashant K. shah, ”Stability analysis of 2-D PSV system represented by Givone–Roesser Model”, ” Department of Electronics Engineering, SVNIT ,Surat chapter, IETE-2015, Gujarat, India.

[9] R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Trans. Automat. Control, vol. 20, pp. 1-10, 1975.

[10] Eric Rogers’The Fornasini-Marchesini Model — its Role in the Analysis and Control of Physical Systems’

[11] Manish Tiwari, Amit Dhawan“A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model”Control Circuits and Systems, January 2012, 3, 17-22 http://dx. Online January 2012.

[12] S. Y. Kung, B. C. Levy, M. Morf, and T. Kailath,"New results in 2-D systems theory, Part II: 2-Dstate-space models – realization and the notionsof controllability, observability, and minimality,”Proc. IEEE, vol. 65, pp. 945-961, 1977.

[13] M. Bisiacco, E. Fornasini, and G. Marchesini, “Dynamic regulation of 2D Systems: A statespace approach,” Linear Algebra and Its Applications, vol. 122/123/124, pp.195-218, 1989.

[14] Tamal Bose, Mei-Qin Chen, and Ratchaneekorn Thamvichai,’ Stability of the 2-D Givone–Roesser Model With Periodic Coefficients’, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 54, NO. 3, MARCH 2007.

[15] R. Thamvichai, T. Bose, D. M. Etter , "2-D periodically shift variant filters without multipliers", Proc. World Multiconf. Systemics Cybernetics and Informatics, vol. 1, 2000-July.

[16] Prashant Shah ,Prof. Haranath Kar, Prof.Vinaya Kumar Srivastava, “Stability Analysis of 2-D PSV Filters described by FM-1 Model” ICECE-2011 IEEE conference at Yi-Cheng, China.

[17] K. Galkowski, "The Fornasini̵Marchesini and the Roesser model: Algebraic methods for recasting", IEEE Trans. Automat. Contr., vol. 41, pp. 107-112, Jan. 1996.

@article{1700143,
      author = {Prashant K Shah},
      title = {A Comparison Between Famous Discrete State Space Models},
      journal = {Iconic Research And Engineering Journals},
      year = {2018},
      volume = {1},
      number = {7},
      pages = {6-13},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1700143.pdf},
      abstract = {n-D system has been very interesting areas from several past decades, due to its various applications. These n-D systems are not easy to represent compare to 1D system. There are several methods that has been used to overcome any problem but among them state space model based methods has accurate solution compare to others. In past few years, Two-dimensional (2-D) discrete Systems have attracted due to their effectiveness in describing systems in several modern engineering fields like image data processing and transformation, thermal processes, water stream heating, etc, out of available space state models.This paper review and compare different 2-D state space models. From comparative analysis we are going to show which model is best usable for which application. And also we have done stability analysis by using our derived criteria and try to conclude the best model in terms of stability.},
      keywords = {Two-dimentional;Control; State-Space; Givone-Roesser(GR); Fornasni-Marchesini(FM)},
      month = {January},
  }