Global stabilization of low-order stochastic nonlinear systems with multiple time-varying delays by a continuous feedback control

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

“…This implies that the stability problem of system (2) cannot be solved by using the classical stochastic system theory (see [33,34]), since the uniqueness of solution is always needed in the application of this theory. Inspired by the deterministic analogs in [22,40] and the delay-free analog in [23,57], the classical stochastic stability concept has been slightly extended in [17] so that it can be applied to more general SNTDSs. In what follows, GSSP and GSASP represent the abbreviation of "globally strongly stable in probability" and "globally strongly asymptotically stable in probability", respectively.…”

“…In what follows, GSSP and GSASP represent the abbreviation of "globally strongly stable in probability" and "globally strongly asymptotically stable in probability", respectively. Definition 1 ( [17]). The trivial solution x = 0 of system ( 2) is GSSP, if there is a class-K function γ x (•) such that P x {|x(t)| ≤ γ x (||ϕ||)} ≥ 1 − ǫ holds for any ǫ > 0 and weak solution x(t), where…”