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To the question of the minimal number of inputs for linear differential algebraic systems

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Abstract

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.

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Author information

Correspondence to A. A. Shcheglova.

Additional information

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).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 442–456, March–April, 2010.

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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

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Keywords

  • differential algebraic equations
  • differential algebraic system
  • controllability
  • minimal number of inputs
  • structural form