Stability of a dynamical system with semi-Markov switchings under conditions of diffusion approximation. (Ukrainian, English) Zbl 1150.93017
Ukr. Mat. Zh. 59, No. 9, 1290-1296 (2007); translation in Ukr. Math. J. 59, No. 9, 1441-1452 (2007).
Summary: 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.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 60J05 | Discrete-time Markov processes on general state spaces |
| 93E15 | Stochastic stability in control theory |
