Singularities of Three-Layered Complex-Valued Neural Networks With Split Activation Function

Event-Triggered Exponential Stabilization for State-Based Switched Inertial Complex-Valued Neural Networks With Multiple Delays

This article explores the exponential stabilization issue of a class of state-based switched inertial complex-valued neural networks with multiple delays via event-triggered control. First, the state-based switched inertial complex-valued neural networks with multiple delays are modeled. Second, by separating the real and imaginary parts of complex values, the state-based switched inertial complex-valued neural networks are transformed into two state-based switched inertial real-valued neural networks. Through the variable substitution method, the model of the second-order inertial neural networks is transformed into a model of the first-order neural networks. Third, an event-triggered controller with the transmission sequence is designed to study the exponential stabilization issue of neural networks constructed above. Then, by constructing the Lyapunov functions and based on some inequalities, we obtain sufficient conditions for exponential stabilization of the proposed neural networks. Furthermore, it is proved that the Zeno phenomenon cannot happen under the designed event-triggered controller. Finally, a simulation example is given to illustrate the correctness of the results.

H∞ estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays

This article is devoted to the H_∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ's formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H_∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.