Some Insights on the Asymptotic Stabilization of a Class of SISO Marginally Stable Systems Using One Delay Block

Abstract

In this paper, the stability of a class of marginally stable SISO systems is studied by applying a single one delay block as a feedback controller. More precisely, we consider an open-loop system with no zeros and whose poles are located exactly on the imaginary axis. Furthermore, a control law formed uniquely by a proportional gain and a delayed behavior is proposed for its closed-loop stabilization. The main ideas are based on a detailed analysis of the characteristic quasi-polynomial of the closed-loop system as the controller parameters (gain, delay) are varied. More precisely, by using the Mikhailov stability criterion, for a fixed delay value, we compute some gain margin guaranteeing the closed-loop stability. The particular case when the characteristic roots of the open-loop system are equidistantly distributed on the imaginary axis is also addressed. Finally, an illustrative example shows the effectiveness of the approach.