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Solutions of matrix equations in problems of mechanics and control

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International Applied Mechanics Aims and scope

The paper considers algorithms for solving linear matrix equations related to problems of mechanics and control, namely, the Lyapunov and Sylvester matrix equations and Riccati-type nonlinear matrix equations. These algorithms are capable of solving both linear equations and linear matrix inequalities. Algorithms based on the Bass relations are used to solve Riccati-type nonlinear matrix equations in so-called special cases where some eigenvalues of the matrix pencil are on a unit circle. These algorithms are compared with those of other authors by way of examples. It is shown that the algorithms can be implemented in symbolic computing routings, which allows solving these equations with high accuracy

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    V. B. Larin

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  1. V. B. Larin
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Correspondence to V. B. Larin.

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Translated from Prikladnaya Mekhanika, Vol. 45, No. 8, pp. 54–85, August 2009.

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Larin, V.B. Solutions of matrix equations in problems of mechanics and control. Int Appl Mech 45, 847–872 (2009). https://doi.org/10.1007/s10778-009-0232-5

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  • DOI: https://doi.org/10.1007/s10778-009-0232-5

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