Application of the second Lyapunov method for getting the conditions of stability in systems with quadratic right-hand side
type: Item
instance of: scholarly article
title: Application of the second Lyapunov method for getting the conditions of stability in systems with quadratic right-hand side
zbMATH Open document ID: 1547.34083
author: Denis Khusainov
author: Andriy Shatyrko
author: B. Půža
author: Veronika Novotná
published in: Ukrainian Mathematical Journal
publication date: 2024-05-15T00:00:00Z
review text: The authors consider an autonomous system with quadratic nonlinearity \(\dot{x}=Ax+S_2(x)\), where \(x\in\mathbb{R}^n\), \(A\) is an asymptotically stable matrix (i.e., all eigenvalues \(\lambda_i(A)\) have a negative real part), \(S_2(x)=X^TBx\) is a quadratic vector-polynome written in the universal vector-matrix form: \(X^T=(X_1^T\cdots X_n^T)\), the matrix \(X_i^T\) has the vector \((x_1,\dots,x_n)\) in \(i\)-th row and all other elements are equal to zero, \(B=\begin{bmatrix} B_1 \\\NB_2\\\N\vdots \\\NB_n \end{bmatrix}\), \(B_i\) is a symmetric matrix, \(i=1,\dots,n\).\N\NAlgebraic sufficient conditions for the global asymptotic stability are presented for the systems of the second and third orders.
reviewed by: Oleg Anashkin
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 7849490
zbMATH Keywords: autonomous systems with a quadratic nonlinearity
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: global asymptotic stability
MaRDI profile type: Publication
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DOI: 10.1007/S11253-024-02300-3
description: scientific article; zbMATH DE number 7849490