Absolute Stabilization of Lur’e Systems by Periodically Intermittent Control

Abstract

In this paper, we design periodically intermittent feedback controllers for Lur’e systems to achieve absolute stabilization. More precisely, our designed periodically intermittent feedback controller is able to cope with any unknown Lur’e-type nonlinearity within a given sector. First, by means of global exponential Lyapunov stability, a set of sufficient stability conditions on the controlled Lur’e system is derived. Subsequently, we give the controller design algorithm in terms of the necessary and sufficient conditions to the stability criteria. By using the LMI Control Toolbox in Matlab, it is easy to compute the control parameters, including the feedback gain matrix, the control period and the control width, involved in the stability criteria. A numerical example considering a Chua’s oscillator under periodically intermittent feedback control is presented to illustrate the validity of our obtained theoretical results. Finally, further discussions close the paper along with some possible interesting topics for future research.