A numerical method for the stability analysis of quasi-polynomial vector fields

被引：15
作者：
Gléria, IM
Figueiredo, A [1 ]
Rocha, TM
机构：
[1] Univ Brasilia, Inst Fis, BR-70910900 Brasilia, DF, Brazil
[2] Univ Catolica Brasilia, Dipartimento Fis, Brasilia, DF, Brazil
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 52卷 / 01期
关键词：
numerical methods; linear matrix inequalities; Lyapunov functions;
D O I：
10.1016/S0362-546X(02)00117-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper shows the sufficient conditions for the existence of a Lyapunov function in the class of quasi-polynomial dynamical systems. We focus on the cases where the system's parameters are numerically specified. A numerical algorithm to analyze this problem is presented, which involves the resolution of a linear matrix inequality (LMI). This LMI is collapsed to a linear programming problem. From the numerical viewpoint, this computational method is very useful to search for sufficient conditions for the stability of non-linear systems of ODEs. The results of this paper greatly enlarge the scope of applications of a method previously presented by the authors. (C) 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：329 / 342
页数：14
相关论文
共 13 条
[1]  
BERGER M, 1987, Geometry I
[2]  
Boyd S., 1994, LINEAR MATRIX INEQUA, DOI https://doi.org/10.1109/jproc.1998.735454
[3]   CONSTRUCTIVE STABILITY AND ASYMPTOTIC STABILITY OF DYNAMICAL-SYSTEMS [J].
BRAYTON, RK ;
TONG, CH .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1980, 27 (11) :1121-1130
[4]   COMPLETE FACTORIZATION AND ANALYTIC SOLUTIONS OF GENERALIZED LOTKA-VOLTERRA EQUATIONS [J].
BRENIG, L .
PHYSICS LETTERS A, 1988, 133 (7-8) :378-382
[5]   Boundedness of solutions and Lyapunov functions in quasi-polynomial systems [J].
Figueiredo, A ;
Gléria, IM ;
Rocha, TM .
PHYSICS LETTERS A, 2000, 268 (4-6) :335-341
[6]   ON THE DETERMINATION OF A DIAGONAL SOLUTION OF THE LYAPUNOV EQUATION [J].
GEROMEL, JC .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1985, 30 (04) :404-406
[7]   Stability properties of a general class of nonlinear dynamical systems [J].
Gléria, IM ;
Figueiredo, A ;
Rocha, TM .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (17) :3561-3575
[8]  
JONHSON CR, 1974, J ECON THEORY, V9, P53
[9]   ON THE EXISTENCE OF POSITIVE DIAGONAL-P SUCH THAT PA+ATP LESS THAN 0 [J].
KHALIL, HK .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1982, 27 (01) :181-184
[10]  
Lasalle J., 1961, Stability by Lyapunov direct method and application
12