## 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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### References:

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