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Robust stability and controllability of stochastic differential delay equations with Markovian switching. (English) Zbl 1040.93069
The authors investigate the almost surely asymptotic stability for nonlinear stochastic differential delay equations with Markovian switching. Most of the existing results on stochastic differential delay equations with Markovian switching are about the moment stability, while little is known on the almost surely asymptotic stability, which is the main topic of the present publication. The results on such stability are then applied to establish a sufficient condition for the controllability of linear stochastic delay equations with Markovian switching. The robust stability is discussed in the last section by using linear matrix inequalities.

93E15 Stochastic stability in control theory
93D09 Robust stability
60J75 Jump processes (MSC2010)
15A39 Linear inequalities of matrices
93B05 Controllability
93D20 Asymptotic stability in control theory
34K50 Stochastic functional-differential equations
Full Text: DOI
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