Stability robustness analysis for state space models

Asymptotically stable linear time-invariant systems under perturbations are considered and analyzed for stability robustness. Based on continuously perturbing the state matrix, instead of solving Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound for the error matrix is obtained under weakly structured perturbations, and the magnitude bounds on the individual elements of the error matrix are obtained under highly structured perturbations. The concept that the perturbed state matrix would actually depend on the operating frequencies is also introduced. The merits of our developed theorems are demonstrated by two examples, and our results are much better than those published in the literature.