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Sib. Zh. Ind. Mat., 2018, Volume 21, Number 3, Pages 104–115 (Mi sjim1015)  

Robust controllability of linear differential-algebraic equations with unstructured uncertainty

P. S. Petrenko

Matrosov Institute of System Dynamics and Control Theory, ul. Lermontovа 134, Irkutsk, 664033 Russia

Abstract: We consider the linear stationary systems of ordinary differential equations (ODEs) that are unsolvedwith respect to the derivative of the unknown vector-function and degenerate identically in the domain of definition. These systems are usually called differential-algebraic equations (DAEs). The measure of how a system of DAEs is unsolved with respect to the derivative is an integer which is called the index of the system of DAEs. The analysis is carried out under the assumption of existence of a structural form with separated differential and algebraic subsystems. We investigate the robust controllability of these systems (controllability in the conditions of uncertainty). The sufficient conditions for the robust complete and $R$-controllability of a system of DAEs with the indices 1 and 2 are obtained.

Keywords: differential-algebraic equations, descriptor system, perturbed system, robust controllability.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00101
Russian Academy of Sciences - Federal Agency for Scientific Organizations II.2
The author was supported by the Russian Foundation for Basic Research (project no. 16-31-00101) and the Siberian Branch of the Russian Academy of Sciences (the Complex Program II.2 of Fundamental Research).


DOI: https://doi.org/10.17377/sibjim.2018.21.310

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:3, 519–530

UDC: 517.926.4+517.977.1+517.922
Received: 23.01.2018

Citation: P. S. Petrenko, “Robust controllability of linear differential-algebraic equations with unstructured uncertainty”, Sib. Zh. Ind. Mat., 21:3 (2018), 104–115; J. Appl. Industr. Math., 12:3 (2018), 519–530

Citation in format AMSBIB
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\by P.~S.~Petrenko
\paper Robust controllability of linear differential-algebraic equations with unstructured uncertainty
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 3
\pages 104--115
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\crossref{https://doi.org/10.17377/sibjim.2018.21.310}
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\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 3
\pages 519--530
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