We examine a control linear system of ordinary differential equations with an identically degenerate matrix coefficient of the derivative of the unknown vector function. We study the question of the minimal dimension of the control vector when the system could be fully controllable on any segment in the domain of definition. The problem is investigated in the cases of stationary systems and the systems with real analytic and smooth coefficients for which some structural forms can be defined.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Gabasov R. and Kirillova F. M., The Qualitative Theory of Optimal Processes [in Russian], Nauka, Moscow (1971).
Gaĭshun I. V., Introduction to the Theory of Linear Nonstationary Systems [in Russian], Izdat. Inst. Mat. NAN Belarus, Minsk (1999).
Campbell S. L. and Petzold L. R., “Canonical forms and solvable singular systems of differential equations,” SIAM J. Algebraic Discrete Methods, No. 4, 517–512 (1983).
Chistyakov V. F., Differential Algebraic Operators with Finite-Dimensional Kernel [in Russian], Nauka, Novosibirsk (1996).
Chistyakov V. F. and Shcheglova A. A., Selected Chapters of the Theory of Differential Algebraic Equations [in Russian], Nauka, Novosibirsk (2003).
Campbell S. L. and Terrell W. J., Observability of Linear Time Varying Descriptor Systems [CRSC Technical Report 072389-01], Center for Research in Scientific Computation, North Carolina Univ. (2003).
Gantmakher F. R., The Theory of Matrices [in Russian], Nauka, Moscow (1988).
Brenan K. E., Campbell S. L., and Petzold L. R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia (1996) (Classics Appl. Math.; 14).
Kunkel P. and Mehrmann V., “Canonical forms for linear differential-algebraic equations with variable coefficients,” J. Comput. Appl. Math., No. 56, 225–251 (1995).
Shcheglova A. A., “Transformation of a linear differential algebraic system to an equivalent form,” in: Proceedings of the IX Chetaev International Conference “Analytical Mechanics, Stability and Motion Control”, Izdat. IDSTU SO RAN, Irkutsk, 2007, 5, pp. 298–307.
Shcheglova A. A., “Control of nonlinear differential algebraic systems,” Avtomat. i Telemekh., No. 10, 57–80 (2008).
Chistyakov V. F. and Shcheglova A. A., “Control of linear differential algebraic systems,” Avtomat. i Telemekh., No. 3, 62–75 (2002).
Original Russian Text Copyright © 2010 Shcheglova A. A.
The author was supported by the Presidium of the Russian Academy of Sciences (Fundamental Research Program No.22, Project 1.7) and the President of the Russian Federation (Grant NSh-1676.2008.1).
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 442–456, March–April, 2010.
About this article
Cite this article
Shcheglova, A.A. To the question of the minimal number of inputs for linear differential algebraic systems. Sib Math J 51, 357–369 (2010). https://doi.org/10.1007/s11202-010-0037-0
- differential algebraic equations
- differential algebraic system
- minimal number of inputs
- structural form