Stabilizing unstable steady states using extended time-delay autosynchronization

We describe a method for stabilizing unstable steady states in nonlinear dynamical systems using a form of extended time-delay autosynchronization. Specifically, stabilization is achieved by applying a feedback signal generated by high-pass-filtering in real time the dynamical state of the system to an accessible system parameter or variables. Our technique is easy to implement, does not require knowledge of the unstable steady state coordinates in phase space, automatically tracks changes in the system parameters, and is more robust to broadband noise than previous schemes. We demonstrate the controller's efficacy by stabilizing unstable steady states in an electronic circuit exhibiting low-dimensional temporal chaos. The simplicity and robustness of the scheme suggests that it is ideally suited for stabilizing unstable steady states in ultra-high-speed systems.