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

Author

Xiaojing Yang ; Zhu, J.J.

Author_Institution

Fac. of Sch. of Electr. Eng. & Comput. Sci., Ohio Univ., Athens, OH, USA

fYear

2014

fDate

4-6 June 2014

Firstpage

3017

Lastpage

3022

Abstract

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.

Keywords

Lyapunov methods; asymptotic stability; invariance; nonlinear control systems; perturbation techniques; time-varying systems; GGM assessment methods; LSM; Lyapunov functions; Lyapunov second method; NLTI systems; exponential stability margin; generalized gain margin assessment; nonlinear time-invariant systems; nonlinear time-varying system; stability metric; time-varying gain perturbations; vanishing regular perturbations; Closed loop systems; Direction-of-arrival estimation; Eigenvalues and eigenfunctions; Lyapunov methods; Symmetric matrices; Time-varying systems; Trajectory; Nonlinear systems; Stability of linear systems; Stability of nonlinear systems;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2014

Conference_Location

Portland, OR

ISSN

0743-1619

Print_ISBN

978-1-4799-3272-6

Type

conf

DOI

10.1109/ACC.2014.6859022

Filename

6859022