Parametric Absolute Stability of Lur'e Systems

Abstract

The concept of parametric absolute stability of Lur'e systems is defined. It provides a mathematical framework for solving the joint problem of feasibility and stability of equilibrium states of Lur'e systems with uncertain parameters and sectorial bounded nonlinearities. This problem arises since stability may be disturbed by the change of equilibrium states which is caused by the parameter variation. In this paper, we consider a single-input single-output Lur'e system, and present Popov-type sufficient conditions for parametric absolute stability. Although the condition contains the parameters, it can be tested by computing the value sets or a family of Popov plots.