Robust Stability of Semi-Markovian Complex-Valued Neural Networks with Generally Uncertain Transition Rates

This paper investigates the stability of complex-valued neural networks (CVNNs) with semi-Markovian jump (sMJ) and generally uncertain transition rates. Each transition rate may be totally unknown or its estimate is determined. Firstly, two improved reciprocally convex inequalities (RCIs) and three less conservative integral inequalities are generalized to the complex-valued domain. Secondly, the existence and uniqueness of the addressed networks are proposed by the complex-valued homeomorphism theorem. Thirdly, by constructing a Lyapunov–Krasovskii functional (LKF), delay-dependent robust stability criteria of the CVNNs are obtained by utilizing the improved complex-valued RCIs and integral inequalities. Finally, simulations are presented to demonstrate the effectivenes and practicality of the established method.