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Lyapunov equations for time-varying linear systems. (English) Zbl 0678.93051
The object of this paper is to give characterizations of the exponential stability of linear time-varying deterministic and stochastic systems in Hilbert spaces, using the Lyapunov differential equations. Generalizations of well-known results of Datko about exponential stability of evolutionary processes are obtained.
Reviewer: M.Megan

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93E15 Stochastic stability in control theory
35B35 Stability in context of PDEs
34D20 Stability of solutions to ordinary differential equations
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