Further results on state feedback stabilization of stochastic high-order nonlinear systems

Abstract

In this paper, a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay. The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.

Adaptive NN output-feedback control for stochastic time-delay nonlinear systems with unknown control coefficients and perturbations

“…where is a positive constant and Ψ 1 (y) = [( ψ 4 + 1)y, 0, y TψT 1 (y)] T . By Assumption 2, (19) and substituting (24)- (27) into (22), one yields…”

“…It is well known that time-delays are frequently encountered in control systems. Recent years have witnessed some developments of stochastic nonlinear time-delay systems based on backstepping, NNs and other design technique, see [2,3,4,5,9,10,18,20,21,22,24,25,26] and [28]. In [3], the decentralized output-feedback control was considered by applying NNs.…”

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

“…In recent years, many results on lower-triangular nonlinear systems has been achieved, see, e.g., [5], [6], [8]- [22], [44]- [48] and the references therein, another important problem is whether these results can also be obtained for stochastic feedforward nonlinear systems.…”

“…Ever since stochastic stability theory is established and improved by [1]- [7], etc., the study of stochastic lower-triangular nonlinear systems based on backstepping design method has achieved remarkable development in recent years, see, e.g., [5], [6], [8]- [22] and the references therein.…”

“…= min 1≤i≤n−1 {γ i1 },b 11 , • • • ,b 14 are positive constants.Similarly, there are positive constantsb22 ,b i3 ,b i4 ,b i5 such that V n (ℵ) ∂η i ∂η j + ∂ 2 W (ℵ) ∂η i ∂η j • |g i | • |g j | ≤b 22 L 1+γ i2 +γ j2 |e i (t)| 4l ,…”