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.


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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