Discrete-time feedback control for highly nonlinear hybrid stochastic systems with non-differentiable delays

This paper is concerned with the stabilization problem for a class of nonlinear hybrid stochastic delay systems. Different from most existing results, the system coefficients are highly nonlinear rather than satisfy the conventional linear growth conditions; the time-varying system delays are no longer required to be differentiable and, moreover, feedback control based on discrete-time state and mode observations, which is more practical and costs less, is employed. By using the Lyapunov functional method, we establish the sufficient stabilization criteria in the sense of exponential stability (both the ¯qth moment stability and the almost sure stability) as well as H∞ stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is also obtained. Finally, a couple of practical food chain models are discussed to illustrate the theoretical results.