Searching Candidate Lyapunov Function with Threshold Accepting Algorithm

Stability of nonlinear systems is a problem of fundamental importance in system engineering. Specifically, the computation of a Lyapunov function which presents one of the tools for study the stability of nonlinear systems. The objective of this work is to study the Lyapunov approaches of polynomial systems. These approaches have been investigated in order to develop numerical algorithms based on the synthesis of a polynomial Lyapunov functions. We proceed in two steps: Firstly, we exploit the Carle man linearization technique which allows achieving a linear system of infinite dimension. Secondly, we implement a Threshold Accepting Algorithm technique to determine a candidate Lyapunov Function. The increase in the degree of truncation of the equation of infinite dimensional of Lyapunov function allowing greater accuracy the theorem of Lyapunov' stability. But it complicates the calculation and synthesis of the expression of the Lyapunov function. The proposed approach is applied to the well known systems.