Dynamic gradient approaches to compute the closest unstable equilibrium point for stability region estimate and their computational limitations

Abstract

The reflected gradient method and the Newton trajectory method are recently emerged approaches to compute the closest unstable equilibrium point (UEP) for stability region estimate. In this note, we address the computational issues involved in these methods. We first suggest a dynamic gradient approach as a unified and extended version of these methods. Then, we show that computing the closest UEP using the dynamic gradient approach can be infeasible.