Global exponential synchronization via nonlinear feedback control for delayed inertial memristor-based quaternion-valued neural networks with impulses

Highlights：

• A nonlinear feedback controller is proposed in the skew field of quaternions to ensure the realization of exponential synchronization.

• Different from the methods used in the existing literature that convert the quaternion-valued system into a complex- or real-valued system, we study the global exponential synchronization of IMQVNNs directly, which avoids increasing the system dimensions and reduces the complexity of analysis.

• Applying differential inclusion theory and the concept of the Filippov solution, some global exponential synchronization criteria are established by Lyapunov stability theory without the conditions of τ˙(t)≤ρ<1 and f(±T)=0. In addition, these LMIs are shown as real-valued, which can be verified by MATLAB directly.

摘要

•A nonlinear feedback controller is proposed in the skew field of quaternions to ensure the realization of exponential synchronization.•Different from the methods used in the existing literature that convert the quaternion-valued system into a complex- or real-valued system, we study the global exponential synchronization of IMQVNNs directly, which avoids increasing the system dimensions and reduces the complexity of analysis.•Applying differential inclusion theory and the concept of the Filippov solution, some global exponential synchronization criteria are established by Lyapunov stability theory without the conditions of τ˙(t)≤ρ<1 and f(±T)=0. In addition, these LMIs are shown as real-valued, which can be verified by MATLAB directly.

论文关键词：Linear matrix inequalities,Inertial memristor-based quaternion-valued neural networks,Global exponential synchronization,Delayed impulses

论文评审过程：Received 15 October 2020, Revised 6 January 2021, Accepted 4 February 2021, Available online 22 February 2021, Version of Record 22 February 2021.