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.

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