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Stability of stochastic jump-parameter semi-Markov linear systems of differential equations. (English) Zbl 1153.60389
Summary: The asymptotic stability of stochastic ItĂ´-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.

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
Full Text: DOI
[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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