Hybrid delay feedback control for mixed H$_\infty$ /passive synchronization of complex dynamical networks with time-varying and mixed coupling delay

Arthit Hongsri, Thongchai Botmart, Wajaree Weera, Narongsak Yotha

Abstract

This paper considers mixed $H_\infty$ and passive synchronization of complex dynamical networks with discrete time-varying delay for a class of mixed coupling and hybrid delay feedback control. The discrete delay is assumed to be interval time-varying delay, which means that the upper and lower bound of delay are adopted. The purpose of this work provided by designing hybrid delay feedback control, which contains error linear term and time-varying delay error linear term, using appropriate Lyapunov-Krasovkii functional (LKF) deal with some new integral inequalities and combined with improved reciprocally convex such that the synchronization error system is exponentially stable with a mixed $H_\infty$ and passive performance index simultaneously. The sufficient conditions are presented in the term of linear matrix inequalities (LMIs). Finally, the effectiveness of our proposed method is employed to demonstrate via numerical example.