Stability Analysis Of Complex-valued Systems With Time Delay

In the field of natural science, most of the researches focus on the field of real numbers, but the application in real-valued domain are greatly limited. In fact, many classic systems and engineering technologies are work in the complex-valued field,such as quantum system and the classical Lorenz equation and communication, image analysis, speech analysis and other engineering fields. In the complex-valued systems modeling, time-delays are inevitable and often made the system performance worse, It could cause the instability and oscillation and even chaos of system. Therefore, in recent years, stability analysis of complex-valued systems with time delay has become a hot topic in the research of nonlinear systems theories, and the researchers have achieved a series of important results. Based on the predecessor’s research, the impulsive stabilization of complex-valued systems with time-delay and stability of memristor-based complex-valued neural networks with time-delay have studied in this paper, and some preliminary results have obtained. Specifically, the main contents and research results in this paper are as follows:1. Impulsive stabilization analysis of complex-valued differential systems with time delayThis paper aims at the dynamics model of complex-valued system with time delay,by designing appropriate impulsive controller, the complex-valued impulsive system with time-delay can be obtained, and through the stability theory of Lyapunov function method and some inequality techniques, some new criteria about global exponential stability of complex-valued systems with time-delay have obtained.2. Stability analysis of memristor-based complex-valued recurrent neural networks with time delayThis paper mainly study on the dynamic properties of memristor-based complex-valued recurrent neural networks with time delay. By using the theory of Lyapunov function method and some inequality techniques, some new criteria about the existence and uniqueness and asymptotic stability conditions of the equilibrium of the system have obtained.