On the stability of slowly time-varying linear systems (Q1894656)

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.