Local stability and performance robustness of nonlinear systems with structured uncertainty

This paper focuses on robust stability and performance of uncertain nonlinear systems with structured locally bounded uncertainty. It is shown that, in a general setting under a considerably mild structural assumption, a local small gain condition implies robust local performance. The feature of this paper is that the performance is defined in a local sense, which is a realistic property inherently nonlinear systems can achieve. The local robustness is analyzed purely in terms of input-output properties so that the proof involves neither state-space descriptions nor Hamilton-Jacobi equations