Event-based Stabilization of Nonlinear Time-Delay Systems

In this paper, a universal formula is proposed for event-based stabilization of nonlinear time-delay systems affine in the control. The feedback is derived from the original one proposed by E. Sontag (1989) and previously extended to event-based control of nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov-Krasovsky functional, it enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtain under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Some simulation results highlight the ability of the proposals