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Number of Parametrization of Discrete-Time Systems without Unit-Delay Element: Single-Input Single-Output Case
Authors: Kazuyoshi Mori
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131455Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 563
 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.
 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.
 S. Shankar and V. Sule, “Algebraic geometric aspects of feedback stabilization,” SIAM J. Control and Optim., vol. 30, no. 1, pp. 11–30, 1992.
 V. Sule, “Feedback stabilization over commutative rings: The matrix case,” SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675–1695, 1994.
 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.
 K. Mori, “Elementary proof of controller parametrization without coprime factorizability,” IEEE Trans. Automat. Contr., vol. AC-49, pp. 589–592, 2004.
 ——, “Parameterization of stabilizing controllers with either rightor left-coprime factorization,” IEEE Trans. Automat. Contr., pp. 1763–1767, 2002.
 ——, “Parametrization of all strictly causal stabilizing controllers,” IEEE Trans. Automat. Contr., vol. AC-54, pp. 2211–2215, 2009.
 M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
 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.
 V. Anantharam, “On stabilization and the existence of coprime factorizations,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 1030–1031, 1985.
 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.
 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.
 ——, “Feedback stabilization of MIMO 3-D linear systems,” IEEE Trans. Automat. Contr., vol. 44, pp. 1950–1955, Oct. 1999.
 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.
 ——, “Controller parameterization of anantharam´s example,” IEEE Trans. Automat. Contr., vol. AC-48, pp. 1655–1656, 2004.
 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.
 V. Kuˇcera, “Stability of discrete linear feedback systems,” in Proc. of the IFAC World Congress, 1975, paper No.44-1.
 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.