Abstract
We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean square with the use of moment equations and Lyapunov stochastic functions.
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References
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Additional information
Kiev National Economic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 776–783, June, 1999.
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Lapshin, A.L. Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input. Ukr Math J 51, 864–873 (1999). https://doi.org/10.1007/BF02591974
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DOI: https://doi.org/10.1007/BF02591974