Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L₂-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.