Intermittent Observer for Chaotic Lur’e Systems With Multi-Nondifferentiable Delay and Partially Limited Output Channels and Its Application to Secure Communication

Abstract

This study focuses on the state tracking problems of chaotic Lur’e systems with nondifferentiable delay and partial channel restriction via intermittent observer. Different from the results obtained by existing chaotic Lur’e systems, the time delay involved in the chaotic Lur’e system explored in this study does not require that the time delay must be differentiable and there is no limit that the time delay must be bounded, which is more in accordance with the operating situation in practical engineering. Subsequently, aiming at the inevitable cyber-attack in the communication network environment, an intermittent observer based on the loss of partial measurement information induced by cyber-attack is constructed. Especially, in the operation process of the designed intermittent estimator, it breaks through the strict requirement that the observation width must be greater than the upper limit of the delay in the existing work, which intuitively reflects the wider application range and has more exploratory significance. Moreover, a meaningful lemma is designed, which effectively overcomes the invalidity of existing Lyapunov function or Lyapunov–Krasovskii functional methods for nondifferentiable systems, and develops novel criteria for partial information loss and nondifferentiable systems, presenting an important theoretical guidance for related topics. Numerical simulations are provided to verify the effectiveness of the proposed intermittent observer mechanism and the stabilization criteria of the error system. Finally, an application of the proposed intermittent observation result for two identical chaotic systems to a secure communication approach is provided.