On the Design of Limit Cycles of Planar Switching Affine Systems

Abstract: In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the phase portraits of the switching systems are determined to obtain globally stable limit cycles from simple specifications, such as given amplitudes and frequencies of desired oscillations. As an application, the paper finally shows that an oscillator model can be derived with a small effort from data measured for an unknown oscillating system.