Global Dissipativity Analysis and Stability Analysis for Fractional-Order Quaternion-Valued Neural Networks With Time Delays
研究了带时滞的分数阶四元数值神经网络的全局耗散性和指数稳定性，通过将四元数模型分解为实值元素并构造Lyapunov泛函，给出了新的判据，并用数值例子验证了方法的有效性。
This article studies dissipativity analysis of fractional-order quaternion-valued neural networks (FOQVNNs) with time delays. Two specific activation functions are considered along with common bounded and activation functions of Lipschitz-kind. Since quaternion multiplication is not commutative, we must divide the model, which is evaluated by quaternion, into four elements that are real-valued elements. On the basis of the construction of novel Lyapunov functional, and applying fractional-calculus theory, new criteria for the test of the global dissipativity and exponential stability of FOQVNNs model are established. FOQVNNs have also been suggested to provide global dissipativity and exponential stability, whereas nonlinear complex activation functions are constrained by the usage of linear matrix inequality methods, which utilize quaternion matrices and positive quaternion definite matrices. Finally, the effectiveness and superiority of the proposed approach is validated through numerical examples.