Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks

The issues of finite time passivity are explored for BAM reaction–diffusion neural networks including discrete delayed and Caputo fractional partial differential operator. With the help of fractional Lyapunov function and existing passivity definition (integral form or fractional integral form), four finite time passivity definitions are given out in Caputo-type fractional derivative form under the double-layer network structure. In this way, the fractional derivative of Lyapunov function can be directly obtained to judge whether the system is passive. Constructing a suitable mixed controller with sign function, several passivity conditions are established as matrix inequality form by utilizing the Green’s theorem, Jensen’s integral inequality, Lyapunov functional approach and four novel definitions. At last, one example is appeared to better illustrate the obtained conditions.