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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
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