Stability analysis of complex-valued nonlinear delay differential systems

Since a quantum system, which is one of the foci of ongoing research, is a classical example of a complex-valued system, in this paper, the issue of asymptotic stability of solutions to complex-valued nonlinear delay differential systems is addressed. By taking advantage of the theory of matrix measure, the exponential stability criteria of a complex-valued nonlinear delay system are established, which not only improve some known results in literature, but also greatly reduce the complexity of analysis and computation. As an application, the exponential stability conditions of 2-dimensional real-valued time-varying delay systems are derived, the conditions are easier to verify in comparison with known results. The effectiveness of the main results are illustrated by some numerical examples.