A Relationship between Two Stabilizing Controllers and Its Application to Two-Stage Compensator Design without Coprime Factorizability – Single-Input Single-Output Case –
In this paper, we first show a relationship between two
stabilizing controllers, which presents an extended feedback system
using two stabilizing controllers. Then, we apply this relationship to
the two-stage compensator design. In this paper, we consider singleinput
single-output plants. On the other hand, we do not assume the
coprime factorizability of the model. Thus, the results of this paper
are based on the factorization approach only, so that they can be
applied to numerous linear systems.
[1] C.A. Desoer, R.W. 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.A. Francis, "Algebraic and
topological aspects of feedback stabilization," IEEE Trans. Automat.
Contr., vol. AC-27, pp. 880-894, 1982.
[3] K. Mori, "Parametrization of all strictly causal stabilizing controllers,"
IEEE Trans. Automat. Contr., vol. AC-54, pp. 2211-2215, 2009.
[4] K. Mori, "Elementary proof of controller parametrization without
coprime factorizability," IEEE Trans. Automat. Contr., vol. AC-49, pp.
589-592, 2004.
[5] M. Vidyasagar, Control System Synthesis: A Factorization Approach,
Cambridge, MA: MIT Press, 1985.
[6] V. Anantharam, "On stabilization and the existence of coprime factorizations,"
IEEE Trans. Automat. Contr., vol. AC-30, pp. 1030-1031,
1985.
[7] V. R. Sule, "Feedback stabilization over commutative rings: The matrix
case," SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675-1695, 1994.
[8] 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.
[9] S. Shankar and V. R. Sule, "Algebraic geometric aspects of feedback
stabilization," SIAM J. Control and Optim., vol. 30, no. 1, pp. 11-30,
1992.
[10] 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.
[11] S. Kodama and N. Suda, Matrix Theory of System Control (in Japanese),
The Society of Instrument and Control Engineers, 1978.
[12] K. Mori, "Capability of two-stage compensator designs ÔÇö single-input
single-output case ÔÇö," in Proceedings of SICE Annual Conference
(SICE 2011), 2011, 288-293.
[1] C.A. Desoer, R.W. 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.A. Francis, "Algebraic and
topological aspects of feedback stabilization," IEEE Trans. Automat.
Contr., vol. AC-27, pp. 880-894, 1982.
[3] K. Mori, "Parametrization of all strictly causal stabilizing controllers,"
IEEE Trans. Automat. Contr., vol. AC-54, pp. 2211-2215, 2009.
[4] K. Mori, "Elementary proof of controller parametrization without
coprime factorizability," IEEE Trans. Automat. Contr., vol. AC-49, pp.
589-592, 2004.
[5] M. Vidyasagar, Control System Synthesis: A Factorization Approach,
Cambridge, MA: MIT Press, 1985.
[6] V. Anantharam, "On stabilization and the existence of coprime factorizations,"
IEEE Trans. Automat. Contr., vol. AC-30, pp. 1030-1031,
1985.
[7] V. R. Sule, "Feedback stabilization over commutative rings: The matrix
case," SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675-1695, 1994.
[8] 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.
[9] S. Shankar and V. R. Sule, "Algebraic geometric aspects of feedback
stabilization," SIAM J. Control and Optim., vol. 30, no. 1, pp. 11-30,
1992.
[10] 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.
[11] S. Kodama and N. Suda, Matrix Theory of System Control (in Japanese),
The Society of Instrument and Control Engineers, 1978.
[12] K. Mori, "Capability of two-stage compensator designs ÔÇö single-input
single-output case ÔÇö," in Proceedings of SICE Annual Conference
(SICE 2011), 2011, 288-293.
@article{"International Journal of Information, Control and Computer Sciences:53413", author = "Kazuyoshi Mori", title = "A Relationship between Two Stabilizing Controllers and Its Application to Two-Stage Compensator Design without Coprime Factorizability – Single-Input Single-Output Case –", abstract = "In this paper, we first show a relationship between two
stabilizing controllers, which presents an extended feedback system
using two stabilizing controllers. Then, we apply this relationship to
the two-stage compensator design. In this paper, we consider singleinput
single-output plants. On the other hand, we do not assume the
coprime factorizability of the model. Thus, the results of this paper
are based on the factorization approach only, so that they can be
applied to numerous linear systems.", keywords = "Relationship among Compensators, Two-Stage Compensator Design, Parametrization of Stabilizing Controllers, Factorization Approach", volume = "7", number = "6", pages = "724-5", }