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Mele, G. (2020) Krylov Methods for Nonlinear Eigenvalue Problems and Matrix Equations. Doctoral Thesis, KTH School of Engineering Sciences, Stockholm.

has been cited by the following article:

• TITLE: Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

  AUTHORS: Tarek Benmiloud

  KEYWORDS: Stability Criterion of Nonlinear Systems, Eigenvectors, State-Space Representation, Lyapunov Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.4, April 28, 2023

  ABSTRACT: In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.