A new trajectory reversing method for estimating stability regions of autonomous nonlinear systems
It is considered an autonomous system \(\dot{x}=f(x)\), with \(x\in \mathbb{R}^{n}, f\in C^{1}\) under the following assumptions: 1. All equilibrium points are hyperbolic. 2. There exists a global Lyapunov function \(V(x)\) such that along any nontrivial solution \(x(t)\) there does not exist a time interval \([t_{1},t_{2}]; t_{1}< t_{2}\) such that \(\dot{V}(x(t))=0\) for \(t\in [t_{1},t_{2}].\) 3. All solutions on the stability boundary remain bounded for \(t>0.\) The method uses a combination of Lyapunov theory, simulation and some properties of the geometric structure of the stability boundary.
scientific article; zbMATH DE number 1487127