Abstract
A controllable linear system of ordinary differential equations not solvable for the derivative of the vector state function of the system is investigated. The coefficient matrix at the derivative of the vector state function is assumed to be degenerate at all points of the domain of definition. Controllability criteria for systems with constant and variable coefficient matrices are formulated in terms of input data.
Similar content being viewed by others
REFERENCES
Dai, L., Singular Control Systems. Lecture Notes in Control and Information Sciences, Berlin: Springer-Verlag, 1989, vol. 118.
Muller, P.C., Stability and Optimal Control of Nonlinear Descriptor Systems: A Survey, Appl. Math. Comput. Sci., 1998, vol. 8, no 2, pp. 269–286.
Chistyakov, V.F., Algebro-differentsial'nye operatory s konechnomernym yadrom (Algebraic Differential Operators with Finite-Dimensional Kernel), Novosibirsk: Nauka, 1996.
Boyarintsev, Yu.E. and Chistyakov, V.F., Algebro-differentsial'nye sistemy. Metody chislennogo resheniya i issledovaniya (Algebraic Differential Systems: Numerical Solution and Investigation Methods), Novosibirsk: Nauka, 1998.
Shcheglova, A.A., Investigation and Solution of Degenerate Systems of Ordinary Differential Equations via Substitution of Variables, Sib. Mat. Zh., 1995, vol. 36, no. 6, pp. 1436–1445.
Boyarintsev, Yu.E., Regulyarnye i singulyarnye sistemy lineinykh obyknovennykh differentsial'nykh uravnenii (Regular and Singular Systems of Linear Ordinary Differential Equations), Novosibirsk: Nauka, 1980.
Campbell, S.L. and Petzold, L.R., Canonical Forms and Solvable Singular Systems of Differential Equations, SIAM J. Alg. Disc. Math., 1983, no. 4, pp. 517–521.
Gantmakher, F.R., Teoriya matrits, Moscow: Nauka, 1988. Translated under the title The Theory of Matrices, New York: Chelsea, 1959.
D'Angelo, H., Linear Time-Varying Systems: Analysis and Synthesis, Boston: Allyn and Bacon, 1970. Translated under the title Lineinye sistemy s peremennymi parametrami. Analiz i sintez, Moscow: Mashinostroenie, 1974.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chistyakov, V.F., Shcheglova, A.A. Controllability of Linear Algebraic Differential Systems. Automation and Remote Control 63, 399–412 (2002). https://doi.org/10.1023/A:1014746232524
Issue Date:
DOI: https://doi.org/10.1023/A:1014746232524