Structured singular value (SSV or µ ) theory is known to be an effective tool for assessing robust stability as well as robust performance for linear time-invariant systems subject to structured uncertainty. Most of the results of the theory deal only with timeinvariant uncertainty. Much less attention has been paid toward the effect of rate-of-variation of time-varying uncertainty upon stability. In this paper, based on the well known robust stability test of real µ theory, we present conditions which explicitly characterize the tradeoff between the allowable perturbation size and the associated allowable rate-of-variation of uncertainty upon stability. With these conditions, lower bound estimates for the two quantities can be computed via the data obtained from the robust stability test.
Journal of Information and Optimization Sciences 28(4), pp.687-702