Stabilization of bilinear systems on the plane by constant and relay controls (Q5942088)

The authors use the method of variable structure control and the notion of equivalent control in order to give a sufficient condition for the global, exponential stabilization of the planar, single-input bilinear system \[ \dot x= Ax+ uBx. \] They also give conditions guaranteeing that the same relay feedback stabilizes the system under consistent perturbations of matrices \(A\), \(B\). Finally, in connection with the stabilization problem, they give a result about state observer reconstruction.