On the characterisation of stability by means of time-delayed feedback control

In this paper we consider the stabilizability of nonlinear dynamical systems via time-delayed state and output feedback control. Based on an eigenvalue optimisation approach in combination with a continuation argument and a result characterising properties of the optimum eigenvalue configurations, we obtain explicit expressions for stabilizability boundaries for two-dimensional systems. As time-delayed feedback can be used to approximate derivative feedback, we also give a comparison of the stabilizability via both types of feedback