Robust Stability for Delay Lur’e Control Systems with Multiple Nonlinearities

For delay Lur’e control systems with multiple non-linearities and time-varying uncertainties, necessary and sufficient conditions for the existence of Lyapunov functional in the extended Lur’e form with negative definite derivative to guarantee robust absolute stability are derived by solving a set of linear matrix inequalities(LMIs). Moreover, some new delay-dependent absolute stability criteria are also presented, in which some free weighting matrices that express the relationships between the terms in Leibniz-Newton formula are considered. Finally, an example is provided to illustrate the effectiveness of the proposed method.