Generalized Gain Margin assessment of Nonlinear Time-Invariant systems via Lyapunov´s Second Method

Generalized Gain Margin (GGM) has recently been introduced as a Gain Margin (GM) like stability metric for nonlinear systems to gauge its exponential stability margin for vanishing regular perturbations. This paper provides GGM assessment methods using Lyapunov´s Second Method (LSM) for Linear Time-Invariant (LTI) systems and Nonlinear Time-Invariant (NLTI) systems, which allows for time-varying gain perturbations. The effectiveness of the method is shown by two concrete examples. The results in this paper could also be extended to linear time-varying and nonlinear time-varying systems using Lyapunov functions for time-varying systems.