Global synchronization in arrays of coupled Lurie systems with both time-delay and hybrid coupling

In this paper, we propose and study an array of coupled delayed Lurie systems with hybrid coupling, which is composed of constant coupling, state delay coupling, and distributed delay coupling. Together with Lyapunov–Krasovskii functional method and Kronecker product properties, two novel synchronization criteria are presented within linear matrix inequalities based on generalized convex combination, in which these conditions are heavily dependent on the upper and lower bounds of state delay and distributed one. Through adjusting inner coupling matrix parameters in the derived results, we can realize the designing and applications of the addressed systems by referring to Matlab LMI Toolbox. The efficiency and applicability of the proposed criteria can be demonstrated by three numerical examples with simulations.