Robust stability criteria for single- and large-scale perturbed systems

Simple time domain criteria for the robust stability or single– and large–scale linear perturbed systems are provided. A bound on the structured perturbation of an asymptotically stable single system is obtained to maintain stability using the concepts of matrix norm and measure. Using the properties of the M–matrix, the result is extended to derive a new criterion for the robust stability of large–scale perturbed systems. The proposed approach does not require the solution of the Lyapunov equation to obtain the allowable bounds for perturbation; the perturbation may be either time–varying or time–invariant.