Abstract
We present a new approach of estimating the asymptotic stability region for nonlinear polynomial discrete systems. This approach is based on the reversing trajectory principle. An approximate reverse system is proposed for polynomial discrete models, and the application of the backward iteration on this system performed from the boundary of an initial estimated domain of stability leads to a large region of asymptotic stability.
The proposed approach has been tested on the known Vander-Pool model, and then applied for a discrete synchronous generator system.