A novel approach to optimize the estimated stability region via energy function for a class of nonlinear dynamical systems in technical models
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https://doi.org/10.54939/1859-1043.j.mst.83.2022.82-94Keywords:
Nonlinear dynamical systems; Stability boundary; Stability region; Optimal energy function.Abstract
The theory of differential equations has been widely known and developed in recent years. Many researchers have drawn attention to the problem of finding the stability region of a nonlinear dynamical system in technical models, which is a complicated issue in the stability theory of dynamical systems. In this problem, how to construct an optimal energy function is considered an essential step to approximate the stability region of a locally stable equilibrium point. The main purpose of this paper is to give a novel approach to optimize the estimated stability region via energy function for nonlinear dynamical models. This ensures that the stability region estimated is optimal in the sense that this estimated region is the largest one characterized by the energy function, which lies entirely in the stability region. Furthermore, numerical experiments are also conducted to compare the difference between the proposed algorithm.
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