Robust stability for delay Lurʹe control systems with multiple nonlinearities

This paper deals with delay Lurʹe 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 Lurʹe 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.