Computation of stability robustness bounds for linear discrete-time systems with time-varying parametric uncertainties

Structured singular value (SSV or mu) 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 time-invariant 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 mu theory, we present conditions which explicitly characterize the trade-off 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.