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Uniform exponential stability for linear discrete time systems with stochastic perturbations. (English) Zbl 1065.93035

Summary: In this paper we give two representations of the solution of linear stochastic discrete-time systems in infinite-dimensional Hilbert spaces and we establish a relation between them. These representations are very important in order to obtain the characterizations of the uniform exponential stability and also to introduce and to characterize the notions of uniform observability and uniform controllability of the systems discussed.

MSC:

93E15 Stochastic stability in control theory
47N70 Applications of operator theory in systems, signals, circuits, and control theory
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