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On the stability of slowly time-varying linear systems. (English) Zbl 0833.93047
The author presents several interesting results on exponential stability of time-varying, finite-dimensional systems $$\dot x(t)= [A(t)+ P(t) ]x(t)$$ provided the perturbation $$P(\cdot)$$ is small and $$t\mapsto A(t)$$ is slowly varying, bounded and the eigenvalues of $$A(t)$$ remain “on average” strictly in the left-half complex plane. These results are also generalized to periodic and stochastic systems.

##### MSC:
 93D20 Asymptotic stability in control theory 93C05 Linear systems in control theory 93E15 Stochastic stability in control theory 93C73 Perturbations in control/observation systems
##### Keywords:
exponential stability; time-varying; perturbation
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