Generalized gain margin for nonlinear systems

Abstract

In this paper, we propose a Generalized Gain Margin (GGM) as a gain margin like stability metric for Nonlinear (NL) systems under regular perturbation. Four time-domain GGM assessment methods for Linear Time-Invariant (LTI) systems are provided, and the GGM equivalence between linear and NL systems, for both time-invariant and time-varying cases, at the equilibrium point is established, which makes it possible to develop GGM assessment methods for NL systems in the subsequent investigation using the corresponding GGM estimating methods for linear systems. However, unlike the linear systems, the GGM of the NL system may be reduced when the size of Domain of Attraction (DOA) is imposed, which is shown by examples. The main results in this paper facilitate generalization to Linear Time-Varying (LTV) systems and Nonlinear Time-Varying (NLTV) systems in future work.