Stability of stochastic jump-parameter semi-Markov linear systems of differential equations. (English) Zbl 1153.60389
Summary: The asymptotic stability of stochastic Itô-type jump-parameter semi-Markov systems of linear differential equations is examined. A system of integral matrix equations is derived which has the property that the existence of a positive definite solution of the system implies the asymptotic stability of the stochastic semi-Markov system. Finally, an illustrative example is presented.
MSC:
| 60K15 | Markov renewal processes, semi-Markov processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E03 | Stochastic systems in control theory (general) |
| 93E15 | Stochastic stability in control theory |
| 34F05 | Ordinary differential equations and systems with randomness |
References:
| [1] | Shmerling E., J. Appl. Probab. 40 pp 442– (2003) · Zbl 1031.60062 · doi:10.1239/jap/1053003555 |
| [2] | Mariton M., Jump Linear Systems in Automatic Control (1990) |
| [3] | Sworder D.D., Estimation Problems in Hybrid Systems (1999) · doi:10.1017/CBO9780511546150 |
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