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.

本文从连续非线性系统吸引域估计的现有方法出发，提出了一种Lyapunov方法，用于估计多项式离散非线性系统的渐近稳定域。从两种不同形式的参数方程出发，我们提出了两种开发方法，目的是确定一个充分的条件以获得二次和三次n的稳定域的一部分。维多项式离散系统。结果包括解决一个多项式方程和无约束的非线性优化问题，其中在二次或三次系统的情况下，可以获得明显的简化。该方法的主要显着优点是其在高维系统上的适用性以及获得接近精确的吸引域极限的椭圆稳定域。说明了两个应用示例，以验证每个开发。