Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Abstract

This paper addresses the problem of enlarging the Domain of Attraction (DA) based on a Generalized Eigenvalue Problem (GEVP) approach. The main contribution is the maximization of the (DA) while characterizing the asymptotic stability region by a Lyapunov Function. Such result is obtained using a Genetic Algorithm (GA). A theoretical proof of the validity of the obtained domain is developed. An illustrative example ends the paper.

An Enhanced Stabilizing Strategy for Switched Nonlinear Systems

“…In this study, a novel nonlinear switched system stabilization strategy will be developed. The strategy is derived from the enlargement of an Attraction Domain for a localized subsystem (Hamidi et al, 2013;Jerbi et al, 2014). The design problem of specifying a subsystem relies on the necessary performance and control law objective considerations.…”

“…The design problem of specifying a subsystem relies on the necessary performance and control law objective considerations. The objective of the latest research is to develop precise techniques in order to enable the maximization of the DA, utilizing the genetic algorithmic (GA) methods as an enhanced optimization approach and also the quasi-convex methods entailing linear matrix inequalities (LMI) (Hamidi et al, 2013;Jerbi et al, 2014). The considered parametric optimization * This paper is an extended version of the paper called "Enlarging the Domain of Attraction in Nonlinear Polynomial Systems", published in the International Journal of Computers Communications and Control, 8(4), 538-547.…”

“…The major purpose of this work is to develop a novel technique for facilitating the stability of a category of nonlinear switched systems. In particular, the objective of this paper is to extend the strategy synthesized in (Hamidi et al, 2013) and to make a full use of the obtained results to achieve the stabilization objective for a class of switched system. Generalized expressions will be given to describe the global stability of nonlinear switched systems.…”

New approach of stability switched nonlinear system

“…The approach proposed by [1] consists to transform the problem into an equivalent problem parameterized by the coefficients of the Lyapunov function. The technique of a quasi-convex Linear Matrix Inequalities (LMI) was used to calculate the lower bound of the maximum DA and the parameter optimizing of the Lyapunov function and the control input parameters were adjusted with Genetic Algorithm.…”

“…The candidate solutions = are chosen arbitrarily and can be regarded as individuals. Each variable can be considered as a gene and the di erent steps of the Genetic Algorithm can be expressed by the different operation of GA[1]: Theorem 2. In this work, a GA is used to estimate the parameters c which is a solution of t he LMI corresponding to this set of parameters.…”