Stabilization of systems with sector bounded nonlinearity by a sawtooth sampled-data feedback

Abstract

The paper considers a nonlinear Lur’e type system with a sector bounded nonlinearity. The zero equilibrium of the system may be unstable, so it is stabilized by a periodically sampled feedback signal. Such stabilization problems were previously explored by a number of researches with the help of the zero-order hold (ZOH) control that is kept constant between successive sampling times. The main disadvantage of this method is that the time delay introduced by ZOH has a destabilizing impact on the closed feedback system, especially in the case when the sampling frequency is sufficiently low and the feedback gain is high. To reduce this effect it is proposed to modify the form of the stabilizing signal. In this paper the reverse sawtooth control is introduced instead of ZOH. The stability criterion is obtained in the form of a feasibility problem for some linear matrix inequalities (LMI). A numerical example demonstrates how the new stabilization method allows to reduce the sampling frequency required for stabilization.