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

Jia, Jinping; Dai, Hao; Zhang, Fandi; Huang, Jianwen

doi:10.1016/j.amc.2022.127234

Cited by 3 publications

(2 citation statements)

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“…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.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…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…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

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

Jia,

Dai,

Zhang

et al. 2024

Nonlinear Dyn

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In this paper, the output feedback stabilization problem is investigated for a class of low-order stochastic nonlinear time-delay systems with the lowertriangular form, where the powers of chained integrators are arbitrary real numbers between 0 and 1, and the multiple time-vary delays act on each system state. Because of the existence of low-order nonlinear terms, the system is not feedback linearizable and differentiable. Nevertheless, we show that an output feedback controller can be systematically designed to ensure the global strong asymptotic stability of the closed-loop system based on an extended stochastic stability theory. In the controller design, the negative effect of the multiple time-varying delays is counteracted by skillfully constructing a novel Lyapunov-Krasovskii functional, and the observer gains are determined by developing a recursive selection procedure. Finally, a numerical example is provided to verified the effectiveness of the proposed method. KeywordsOutput feedback stabilization • Low-order nonlinearities • Stochastic nonlinear systems • State observer • Multiple time-varying delays J. Jia ( ) • F. Zhang ( ) •

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Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

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

Jia,

Dai,

Zhang

et al. 2024

Nonlinear Dyn

Self Cite

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Design stabilisers for multi-input affine control stochastic systems via stochastic control Lyapunov functions

Himmi,

Oumoun

2024

International Journal of Control

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

Jia,

Dai,

Zhang

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, the output feedback stabilization problem is investigated for a class of low-order stochastic nonlinear time-delay systems with the lower-triangular form, where the powers of chained integrators are arbitrary real numbers between 0 and 1, and the multiple time-vary delays act on each system state. Because of the existence of low-order nonlinear terms, the system is not feedback linearizable and differentiable. Nevertheless, we show that an output feedback controller can be systematically designed to ensure the global strong asymptotic stability of the closed-loop system based on an extended stochastic stability theory. In the controller design, the negative effect of the multiple time-varying delays is counteracted by skillfully constructing a novel Lyapunov-Krasovskii functional, and the observer gains are determined by developing a recursive selection procedure. Finally, a numerical example is provided to verified the effectiveness of the proposed method.

show abstract

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

Cited by 3 publications

References 41 publications

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

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

Design stabilisers for multi-input affine control stochastic systems via stochastic control Lyapunov functions

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

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