Stability and robustness of slowly time-varying linear systems

A well known result for finite-dimensional time-varying linear systems is that if each ´frozen time´ system is stable, then the time-varying system is stable for sufficiently slow time-variations. These results are reviewed and extended to a class of Volterra integrodifferential equations, specifically, differential equations with a convolution operator in the right-hand-side. The results are interpreted in the context of robustness of time-varying linear systems with a special emphasis on analysis of gain-scheduled control systems.