Stability of a dynamical system with semi-Markov switchings under conditions of diffusion approximation
We obtain sufficient conditions for the stability of a dynamical system in a semi-Markov medium under the conditions of diffusion approximation by using asymptotic properties of the compensation operator for a semi-Markov process and properties of the Lyapunov function for an averaged system.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 9, pp 1441-1452.
Citation Example: Chabanyuk Ya. M. Stability of a dynamical system with semi-Markov switchings under conditions of diffusion approximation // Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1290–1296.