Uniform exponential stability and uniform observability of time-varying linear stochastic systems in Hilbert spaces. (English) Zbl 1062.60064

Ungureanu, Viorica Mariela

Gaşpar, D. (ed.) et al., Recent advances in operator theory, operator algebras, and their applications. Proceedings of the 19th international conference on operator theory (OT 19), Timişoara, Romania, June 27–July 2, 2002. Basel: Birkhäuser (ISBN 3-7643-7127-7/hbk). Operator Theory: Advances and Applications 153, 287-306 (2005).

Summary: The main object of this paper is to discuss the problem of the uniform exponential stability and uniform observability of time-varying linear stochastic equations in Hilbert spaces. We give a representation of the covariance operator associated to the mild solutions of these equations which allow us to obtain a characterization of the uniform exponential stability of uniformly observable systems in terms of Lyapunov equations.
For the entire collection see [Zbl 1051.46002].

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35B40	Asymptotic behavior of solutions to PDEs
93B07	Observability

Keywords:

stochastic differential equation; uniform exponential stability; uniform observability; Lyapunov equation