Stability of complex-valued impulsive system with delay

Since many systems such as quantum system, complex-valued neural network and Lorenz system are complex-valued differential system, in this paper, the stability of complex-valued impulsive system with delay is addressed. By taking advantage of Lyapunov function in complex field, some new criteria for global exponential stability are established, which not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. As an application, a new impulsive controller for complex-valued Lü system with delay is designed.