Robust Stability under Additive Perturbations: An Implicit Assumption

摘要

The algebraic robust stability result of Bhaya and Desoer (1985) is discussed. Bhaya and Desoer derived a necessary and sufficient condition for the U-stability of a multiple input/multiple output linear time invariant system under arbitrary perturbations, where U denotes an undesirable symmetric region of the complex plane, and includes at least the closed right half plane. It is shown that their result implicity assumes that the total number of poles in U of the perturbed plant is equal to the total number of poles in the nominal plant plus the total number of poles in U of the perturbation.