Linear time-varying stochastic differential equations with a.s. continuous, convergent random system matrix processes are considered. We show that given the limit is known to be Hurwitz (i.e. asymptotically stable), the generated state solutions are a.s. bounded. This property is shown to hold by substantiating that, w.p.1, (i) no finite escape time exists and (ii) no divergence to infinity, as t goes to infinity, may occur. We end with an adaptive control application example.

Based on a joint work with Peter E. Caines

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