A Lyapunov approach for attraction domain estimation of polynomial discrete nonlinear systems with quadratic and cubic terms

Abstract

In this paper, we propose a Lyapunov method for estimating asymptotic stability domain of polynomial discrete nonlinear systems, drawn from an existing approach for attraction domain estimation of continuous nonlinear systems. Proceeding from two different forms of a parametric equation, we present two development methods with the aim of identifying a sufficient condition to obtain a part of the stability domain for quadratic and cubic n-dimensional polynomial discrete systems. The results consist in solving a polynomial equation and unconstrained nonlinear optimization problems, where in case of quadratic or cubic systems, significant simplifications are obtained. The main notable advantages of this approach are its applicability on high-dimensional systems and obtaining an ellipsoidal stability domain which approaches the exact attraction domain limits. Two application examples are illustrated to validate each development.