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On the stability of one dimensional discrete-time jump linear systems

Czornik A., Nawrat A., Rabsztyn S.

Archives of Control Sciences

2003

Vol. 13, no. 1

81-93

In this paper we present necessary and sufficient conditions for "delta" - moment stability and almost sure stability of one-dimensional discrete-time linear systems subject is equivalent to "delta"-moment stability for certain "delta">0.

Almost sure and moment stability of stochastic partial differential equations

Kwiecińska A. A.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 2

405--415

We study the almost sure and moment stability of a class of stochastic partial differential equations and we present an infinite-dimensional version of a theorem proved for stochastic ordinary differential equations by Arnold, Oeljeklaus and Pardoux. We also investigate how adding a term with white noise influences the stability of a deterministic system. The outcome is quite surprising. It turns out that regardless whether the deterministic system was stable or unstable, after adding a term with sufficiently large noise, it becomes pathwise exponentially stable and unstable in the p-th mean for p >1.