Improvement master–slave robustly synchronous criteria of uncertain chaotic Lur’e systems via an augmented Lyapunov–Krasovskii functional

Abstract

The robust synchronization of uncertain master–slave Lur’e systems based on time-delayed feedback control is further investigated. A less conservative synchronization stability criterion and a less conservative robust synchronization stability criterion than some recent published references are proposed via Lyapunov stability theory. First, an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed, where some single integral terms are augmented to the integrand component of a single-integral subfunction. This not only increases some coupling information on some system variables but also increases the coupling information on some necessary variables contained in the inequality lemmas, which can make full use of the inequality lemmas and reduce the conservatism of the synchronization stability criterion. Second, to overcome the nonlinear phenomena in the synchronization criterion, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequalities to the linear matrix inequalities (LMIs) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach.