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Evaluation of the reachability subspace of general form polynomial matrix descriptions (PMDs). (English) Zbl 0829.93014
Reachability of linear continuous systems described by a polynomial matrix description is considered. This enables treating jointly regular as well as singular systems. The problem of admissible initial conditions is highlighted, and reachable subspaces are investigated. Simple reachability tests are provided.

MSC:
93B25 Algebraic methods
93B03 Attainable sets, reachability
93C05 Linear systems in control theory
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References:
[1] S. L. Cambell C. D. Meyer, N. Rose: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAM J. Appl. Math. 31 (1976), 3, 411-425. · Zbl 0341.34001
[2] D. Cobb: Descriptor Variable and Generalized Singularly Pertubed Systems: A Geometric Approach. Ph.D. Dissertation, Dept. of Electrical Engineering, Univ. of Illinois 1980.
[3] D. Cobb: Feedback and pole placement in descriptor-variable systems. Internat. J. Control 33 (1981), 6, 1135-1146. · Zbl 0464.93039 · doi:10.1080/00207178108922981
[4] D. Cobb: Controllability, observability, and duality in singular systems. IEEE Trans. Automat. Control AC-29 (1984), 12, 1076-1082.
[5] D. Cobb: On the solution of linear differential equations with singular coefficients. J. Differential Equations 46 (1982), 310-323. · Zbl 0489.34006 · doi:10.1016/0022-0396(82)90097-3
[6] G. F. Fragulis: A closed formula for the determination of the impulsive solutions of linear homogeneneous matrix differential equations. IEEE Trans. Automat. Control AC-38 (1993), 11, 1688-1695. · Zbl 0790.93066
[7] G. F. Fragulis: Analysis of Generalized Singular Systems. Ph.D. Dissertation, Department of Mathematics, Aristotle Univ. of Thessaloniki 1990.
[8] K. Ozcaldiran: Control of Descriptor Systems. Ph.D. Dissertation, School of Electrical Engineering, Georgia Institute of Technology, Atlanta, GA 1985. · Zbl 0606.93017
[9] A. I. G. Vardulakis: Linear Multivariable Control: Algebraic Analysis and Synthesis Methods. Wiley, New York 1991. · Zbl 0751.93002
[10] A. I. G. Vardulakis, G. F. Fragulis: Infinite elementary divisors of polynomial matrices and impulsive solutions of linear homogeneous matrix differential equations. Circuits Systems Signal Process. 8 (1989), 3, 357-373. · Zbl 0678.34002 · doi:10.1007/BF01598420
[11] E. Yip, R. Sincovec: Solvability, controllability, and observability of continuous descriptor systems. IEEE Trans. Automat. Control AC-26 (1981), 3, 702-707. · Zbl 0482.93013 · doi:10.1109/TAC.1981.1102699
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