Event-Triggered Control of Stochastic Functional Differential Systems via Degenerate Lyapunov Functionals

This article discusses the problem of event-triggered controls (ETCs) for stochastic functional differential systems (SFDSs). For the stabilization of SFDSs, we design a proper degenerate Lyapunov functional and propose a novel ETC. The degenerate Lyapunov functional is more general than the traditional positive definitive Lyapunov functionals and ETC has a prominent advantage of reducing communication resources compared with periodic sampled-data feedback controls because time updating is based on a certain event. Also, a fixed positive lower bound on the stochastic interexecution times is guaranteed by this novel event-triggering mechanism. Together with ETC and the degenerate Lyapunov functional, the boundedness, mean square exponential stabilization, and globally asymptotical stabilization of SFDSs can be established for different choices of parameters. Finally, the obtained results are validated through numerical simulations.