Global μ-stability analysis of discrete-time complex-valued neural networks with leakage delay and mixed delays

In this paper, the problem of μ-stability for discrete-time complex-valued neural networks with three kinds of time-delays including leakage delay, discrete delay and distributed delay is considered. Based on contraction mapping theorem and homeomorphism mapping theorem in complex domain, some sufficient conditions are proposed for the existence and uniqueness of the equilibrium point of the addressed neural networks. By constructing an appropriate Lyapunov–Krasovskii functional, and employing the matrix inequality techniques, several delay-dependent criteria for checking the global μ-stability of the complex-valued neural networks are established in linear matrix inequalities (LMIs), which can be checked numerically using the effective YALMIP Tool in MATLAB. As direct applications of these results, we get some criteria on the exponential stability, power-stability and log-stability of the neural networks.