Backward iteration approaches for the stability domain estimation of discrete non-linear polynomial systems

This paper deals with two evolutionary algorithms for calculating the asymptotic stability region for discrete non-linear polynomial systems. These algorithms rest on two new approaches of inverting discrete direct polynomial state equation. Based on some topological considerations, the systematic computational algorithms are then applied on the second-order polynomial model of a synchronous generator power system. Hence, a comparative study is presented to illustrate the benefits of the proposed algorithms so as to maximise the Region of Asymptotic Stability (RAS).