Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32146
Number of Parametrization of Discrete-Time Systems without Unit-Delay Element: Single-Input Single-Output Case

Authors: Kazuyoshi Mori


In this paper, we consider the parametrization of the discrete-time systems without the unit-delay element within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters. We consider single-input single-output systems in this paper. By the investigation, we find, on the discrete-time systems without the unit-delay element, three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: Linear systems, parametrization, Coprime Factorization, number of parameters.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 661


[1] C. Desoer, R. Liu, J. Murray, and R. Saeks, “Feedback system design: The fractional representation approach to analysis and synthesis,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 399–412, 1980.
[2] M. Vidyasagar, H. Schneider, and B. Francis, “Algebraic and topological aspects of feedback stabilization,” IEEE Trans. Automat. Contr., vol. AC-27, pp. 880–894, 1982.
[3] S. Shankar and V. Sule, “Algebraic geometric aspects of feedback stabilization,” SIAM J. Control and Optim., vol. 30, no. 1, pp. 11–30, 1992.
[4] V. Sule, “Feedback stabilization over commutative rings: The matrix case,” SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675–1695, 1994.
[5] K. Mori and K. Abe, “Feedback stabilization over commutative rings: Further study of coordinate-free approach,” SIAM J. Control and Optim., vol. 39, no. 6, pp. 1952–1973, 2001.
[6] K. Mori, “Elementary proof of controller parametrization without coprime factorizability,” IEEE Trans. Automat. Contr., vol. AC-49, pp. 589–592, 2004.
[7] ——, “Parameterization of stabilizing controllers with either rightor left-coprime factorization,” IEEE Trans. Automat. Contr., pp. 1763–1767, 2002.
[8] ——, “Parametrization of all strictly causal stabilizing controllers,” IEEE Trans. Automat. Contr., vol. AC-54, pp. 2211–2215, 2009.
[9] M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
[10] K. Mori, “Coprime factorizability and stabilizability of plants extended by zeros and parallelled some plants,” Engineering Letters, vol. 24, no. 1, pp. 93–97, 2014.
[11] V. Anantharam, “On stabilization and the existence of coprime factorizations,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 1030–1031, 1985.
[12] K. Mori, “Parameterization of stabilizing controllers over commutative rings with application to multidimensional systems,” IEEE Trans. Circuits and Syst. I, vol. 49, pp. 743–752, 2002.
[13] Z. Lin, “Output feedback stabilizability and stabilization of linear n-D systems,” in Multidimensional Signals, Circuits and Systems, K. Galkowski and J. Wood, Eds. New York, NY: Taylor & Francis, 2001, pp. 59–76.
[14] ——, “Feedback stabilization of MIMO 3-D linear systems,” IEEE Trans. Automat. Contr., vol. 44, pp. 1950–1955, Oct. 1999.
[15] K. Mori, “Number of parameters of anantharam’s model with single-input single-output case,” in Proceedings of The 18th International Conference on Automatic Control, Telecommunications, Signals and Systems (ICACTSS 2016), 2016, 349–353.
[16] ——, “Controller parameterization of anantharam´s example,” IEEE Trans. Automat. Contr., vol. AC-48, pp. 1655–1656, 2004.
[17] D. Youla, H. Jabr, and J. Bongiorno, Jr., “Modern Wiener-Hopf design of optimal controllers, Part II: The multivariable case,” IEEE Trans. Automat. Contr., vol. AC-21, pp. 319–338, 1976.
[18] V. Kuˇcera, “Stability of discrete linear feedback systems,” in Proc. of the IFAC World Congress, 1975, paper No.44-1.
[19] F. Aliev and V. Larin, “Comments on “optimizing simultaneously over the numerator and denominator polynomials in the youla-kucera parameterization”,” IEEE Trans. Automat. Contr., vol. 52, no. 4, p. 763, 2007.