Robust stability for delay Lur'e control systems with multiple nonlinearities

This paper deals with delay Lur'e control systems with multiple nonlinearities and time-varying structured uncertainties. First, some sufficient, and necessary and sufficient conditions for the existence of a Lyapunov functional in the extended Lur'e form with a negative definite derivative that guarantees delay-independent robust absolute stability are presented. Then, some new less conservative delay-dependent absolute stability criteria are derived that employ free weighting matrices to express the relationships between the terms in the Leibniz-Newton formula. All the criteria are based on linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the method.