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On a criterion for the complete controllability of nonautonomous linear systems

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Abstract

We describe the controllability sets of linear nonautonomous systems ẋ = A(t)x + B(t)u, x ∈ ℝn, u ∈ U ⊆ ℝm, with entire matrix functions A(t) and B(t) and with a linear set U of control constraints. We derive a criterion for the complete controllability of these linear systems in terms of derivatives of the entire matrix functions A(t) and B(t) at zero. This complete controllability criterion is compared with the Kalman and Krasovskii criteria.

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Authors and Affiliations

  1. Chuvash State University, Cheboksary, Russia

    Yu. M. Semenov

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  1. Yu. M. Semenov
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Original Russian Text © Yu.M. Semenov, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 11, pp. 1646–1652.

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Semenov, Y.M. On a criterion for the complete controllability of nonautonomous linear systems. Diff Equat 47, 1668–1674 (2011). https://doi.org/10.1134/S0012266111110139

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  • DOI: https://doi.org/10.1134/S0012266111110139

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