Stability Analysis of Linear Continuous-Time Delay-Difference Systems with Three Delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with three 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 three delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. A numerical example is provided to demonstrate the effectiveness and less conservativeness of the proposed method.