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This paper considers connections between bounded-input, bounded-output stability and asymptotic stability in the sense of Lyapunov for linear time-varying systems. By modifying slightly the definition of bounded-input, bounded-output stability, an equivalence between the two types of stability is found for systems which are uniformly completely controllable and observable. The various matrices describing the system need not be bounded. Other results relate to the characterization of uniform complete controllability and the derivation of Lyapunov functions for linear time-varying systems.
Anderson et al. (Fri,) studied this question.