A note on the genericity of simultaneous stabilizability and pole assignability
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In this paper we study the genericity of simultaneous stabilizability, simultaneous strong stabilizability, and simultaneous pole assignability, in linear multivariable systems. The main results of the paper had been previously established by Ghosh and Byrnes using state-space methods. In contrast, the proofs in the present paper are based on input-output arguments, and are much simpler to follow, especially in the case of simultaneous and simultaneous strong stabilizability. Moreover, the input-output methods used here suggest computationally reliable algorithms for solving these two types of problems. In addition to the main results, we also prove some lemmas on generic greatest common divisors which are of independent interest.
- 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. Control,25, 399–412, 1980.
- M. Vidyasagar, H. Schneider, and B. A. Francis, Algebraic and topological aspects of feedback stabilization,IEEE Trans. Automat. Control,27, 880–895, 1982.
- D. C. Youla, J. J. Bongiorno, Jr. and C. N. Lu, Single-loop feedback stabilization of linear multivariable plants,Automatica,10, 159–173, 1974.
- M. Vidyasagar and N. Viswanadham, Algebraic design techniques for reliable stabilization,IEEE Trans. Automat. Control,27, 1085–1094, 1982.
- B. K. Ghosh and C. I. Byrnes, Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation,IEEE Trans. Automat. Control,28, 735–741, 1983.
- M. Vidyasagar,Control System Synthesis: A Factorization Approach, M.I.T. Press, Cambridge, MA, 1985.
- M. Vidyasagar, The graph metric for unstable plants and robustness estimates for feedback stability,IEEE Trans. Automat. Control,29, 403–418, 1984.
- B. K. Ghosh, Simultaneous stabilization and pole placement of a multimode linear dynamical system, Ph.D. thesis, Harvard University, 1983.
- K. D. Minto and M. Vidyasagar, A state-space approach to simultaneous stabilization,Control: Theory Adv. Technol.,2, 39–64, 1986.
- A note on the genericity of simultaneous stabilizability and pole assignability
Circuits, Systems and Signal Processing
Volume 5, Issue 3 , pp 371-387
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- 1. Department of Electrical Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario
- 2. Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts
- 3. School of Automation, Indian Institute of Science, 560 012, Bangalore, India