Effect of leakage time-varying delay on stability of nonlinear differential systems

In this paper, a class of nonlinear differential systems with leakage time-varying delay is considered. Sufficient conditions for the existence-uniqueness and global asymptotic stability of the equilibrium point are derived by using fixed point theorems, Lyapunov-Krasovskii functional and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of a linear matrix inequality (LMI), which can be efficiently solved via standard numerical software. Even for the case of leakage constant delay, the criterion is shown to be less conservative than a recent publication. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.