Semi‐Global Impulsive Exponential Stability of Stochastic Complex‐Valued Complex Networks With Distributed Delay and Semi‐Markov Jump

ABSTRACT In this article, we focus on how to achieve semi‐global exponential stability of stochastic complex‐valued complex networks with distributed delay and semi‐Markov jump (SCVCNDDSMJ) under impulse control. Considering complex‐valued systems, stochastic disturbance, and semi‐Markov jump, the segment functions in the Banach space are redefined and Driver's derivative for the functionals are redefined basically. Considering complex networks, we construct a global functional by the solution component to the exponentially stabilized continuous time feedback control systems and some quasi‐properties of are derived. Combining impulse differential inequalities and mathematical induction, semi‐global impulsive exponential stability can be obtained when acts on the solution of the impulse control systems. We also provide some semi‐global impulsive exponential stability criteria including the estimates of the average impulse control interval, the upper bound of the impulse control gain, and the expression between the bound of the initial condition and the maximum impulse interval without imposing restrictions on the bound of the initial condition. Moreover, the theoretical results obtained are utilized in a kind of stochastic complex‐valued recurrent neural networks. In the end, the validity of the obtained theoretical results is confirmed by corresponding numerical simulations.