Lyapunov function of general Lurie systems with multiple nonlinearities Original Research Article

In this paper, the absolute stability problem of general Lurie control system with multiple nonlinearities is investigated. Some new necessary and sufficient conditions are obtained for the existence of Lyapunov function of extended Lurie form with negative definite and negative semidefinite derivatives. From these conditions, some very general algebraic criteria for absolute stability are obtained, which extend and generalize previous work on the subject. A numerical example is presented to illustrate the effectiveness of the new criteria.