Delay-dependent passivity of impulsive coupled reaction–diffusion neural networks with multi-proportional delays.

This article deals with passivity of coupled reaction–diffusion neural networks (CRDNNs) with multi-proportional delays and impulses. Two aspects are mainly considered: one is that the coupling term of the system depends on the delay, and the other is that the coupling term of the system is delay-independent. In order to simplify the complex system, the Kronecker product and its properties are applied to rewrite the complex system. According to whether the transfer function is a multi-proportional delayed function or a single proportional delayed function, several seemly Lyapunov Krasovskii functionals (LKFs) are constructed. Then, through the use of Kronecker product, Green's formula and inequality analysis method, several criteria of input-strictly passivity (ISP) and output-strictly passivity (OSP) of the studied systems are attained, which all rely on proportional delayed factors. In addition, these criteria are exhibited in the form of matrix inequalities and can be checked with conventional software. Eventually, the passivity criteria are validated by two numerical examples and simulations. • Without the use of nonlinear transformations, the structure of paper is clearer. • Kronecker product and properties simplify the computational process of the paper. • The influence of impulses is considered, which is better describe the studied system. • These passive criteria are exhibited in the form of LMI and are easy to check. [ABSTRACT FROM AUTHOR]