Controlling Fractional Difference Equations Using Feedback

Abstract

One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations under feedback. The stability results are derived for an arbitrary feedback time $\tau$. We study the cases of $\tau=1$ and $\tau=2$ in further detail. The extension to the stability of fixed points under feedback for nonlinear fractional order difference equations with fixed points $ x_{*}=0$ is also carried out.