Analysis of local performance robustness of nonlinear systems with structured uncertainty

This paper is concerned with the analysis problem of robust performance of nonlinear systems with structured locally bounded uncertainty. Both discrete-time and continuous-time systems arc studied. The performance is defined in a local sense, which is a realistic property inherently-nonlinear systems can achieve. This paper presents that, in a general setting under a considerably mild structural assumption, a local small gain condition implies robust local performance. The robustness is analyzed purely in terms of input-output properties so that the proof involves neither state-space description nor Hamilton-Jacobi inequality nor construction of destabilizing perturbation.