LMI approach to stability analysis of Cohen-Grossberg neural networks with \(p\)-Laplace diffusion (Q1952877)

Summary: The nonlinear \(p\)-Laplace diffusion (\(p > 1\)) was considered in the \textit{M.A. Cohen} and \textit{S. Grossberg} neural network (CGNN) model [IEEE Trans. Syst. Man Cybern. 13, 815--826 (1983; Zbl 0553.92009)] , and a new linear matrix inequalities (LMI) criterion is obtained, which ensures that the equilibrium of the CGNN is stochastically exponentially stable. Note that, if \(p = 2\), the \(p\)-Laplace diffusion is just the conventional Laplace diffusion in many previous papers. It is worth mentioning that even if \(p = 2\), the new criterion improves some recent ones due to the computational efficiency. In addition, the resulting criterion has advantages over some previous ones in that both the impulsive assumption and diffusion simulation are more natural than those of some recent papers.