LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter

In this paper, a class of singularly perturbed nonlinear impulsive delay differential systems is considered, where the time delays include a small parameter. Based on Lyapunov–Krasovskii functional and free weighting matrix method, some novel delay-dependent global asymptotic stability results are derived in terms of linear matrix inequalities (LMIs) which can be easily solved using efficient convex optimization algorithms. The results show that the system stability is very sensitive to the singular perturbation and the small parameter in time delays. A numerical example is given to show the effectiveness of the proposed results.