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

Abstract

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.