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

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.