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Input-to-state stable synchronization for delayed Lurie systems via sampled-data control

This paper focuses on the input-to-state stable (ISS) synchronization issue for delayed Lurie systems via sampled-data control. Two time-dependent Lyapunov functionals are constructed for delay functions without and with differentiability restrictions, respectively. Sufficient conditions on the ISS synchronization are established via using the proposed Lyapunov functionals, the reciprocally convex-combination approach, and a few integral inequalities. The gain matrix of the needed sampled-data controller can be attained through solving a couple of linear matrix inequalities, which is numerically easy to handle. Furthermore, the present conditions are capable of ensuring the exponential synchronization of the considered Lurie systems in the absence of external disturbances. In the end, two examples are employed to demonstrate the effectiveness of the established ISS synchronization conditions.