Intermittent Control for Synchronization-Like Behavior of State-Dependent Impulsive Neural Networks via Interval–Impulse Differential Inequality

This paper investigates the synchronization problem for a class of master–slave neural networks with state-dependent impulses. Different from fixed-time impulsive systems, the impulsive instants considered here depend on the current states of the neural networks, which makes the synchronization analysis more complicated. In particular, when both the master and slave systems possess their own state-dependent impulses, the corresponding impulsive instants are generally asynchronous, so the synchronization error evolves over an impulsive interval rather than undergoing only a single instantaneous jump. To address this difficulty, two easily verifiable conditions are first proposed to guarantee that each trajectory intersects every impulsive surface exactly once, thereby excluding the beating phenomenon. Then, an interval–impulse differential inequality is established to characterize the error evolution on non-impulsive subintervals and to handle the mismatch between the impulsive times of the master and slave systems. Based on this inequality, an intermittent controller activated only outside the impulsive interval is designed so that the controller does not destroy the intrinsic state-dependent impulsive rhythm of the master system. By combining Lyapunov analysis with matrix inequality techniques, verifiable criteria are derived for local exponential synchronization-like behavior of the considered neural networks. Here, synchronization-like refers to exponential decay of the synchronization error on the non-mismatched time intervals since the master and slave systems generally possess asynchronous state-dependent impulsive instants. Finally, numerical examples are presented to illustrate the effectiveness of the proposed conditions and control strategy. The simulation results show that the designed controller can effectively suppress synchronization error and that increasing the control gain can significantly accelerate the convergence process.