Stabilization of an overturned pendulum with delayed feedback
The goal of the paper is to construct a domain of asymptotic stability of the zero solution to the differential equation \[ \ddot\varphi(t) + \dot\varphi(t-\tau) cos\varphi(t) + a\varphi(t-\tau)\cos\varphi(t) - b\sin\varphi(t)=0 \] in the plane of combined parameters \(a>b\) and \(b>0\) for fixed \(\tau\). The construction is made by the method of \(D\)-partitionings.
scientific article; zbMATH DE number 1974908