Exploiting Structures of Noiilinesr Parametric Pertiirbations for Robust Stability

Tlie research on robust stability of uncertain systems has been undertaking for a number of years. We now seem to have a good understanding of the socalled linear (or affine) perturbations. The progress for tackling nonlinear perturbations has been relatively slow due to obvious difficulties. One approach to nonliiiear perturbations is to convert the robust stability problem into a certain type of nonlinear programining probleni. The deficiencies of this approach are the nuirierical iuefficieiicy and the lack of a d y t i c a l insights. This paper is meant to emphasize the advairtages of exploiting special structures of nonlinear perturbations for robust stability. This is motivated by the fact that in many practical situations nonlinear perturbations are parameterized in a simple manner, such as uncertainties in the zeros, poles and gains of a transfer function, serial interconnections of perturbed subsystems, and uncertain time-delay constants. We exam tliese coinnionly used structures of nonlinear perturbations and provide efficient tests for robust stability.