Stability criteria of stochastic nonlinear systems with asynchronous impulses and switchings

Jiao, Ticao; Park, Ju H.; Zong, Guangdeng

doi:10.1007/s11071-019-04960-4

Cited by 19 publications

(2 citation statements)

References 33 publications

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“…The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of dynamical systems, see [1,2], in particular, of stochastic systems, see [10,11,17,27].…”

Section: Introductionmentioning

confidence: 99%

New stability criteria for stochastic perturbed singular systems in mean square

2021

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In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. Sufficient conditions on uniform exponential stability and practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems are obtained based upon Lyapunov techniques. Furthermore, we study the problem of stability and stabilization of some classes of stochastic singular systems. Eventually, we provide a numerical example to validate the effectiveness of the abstract results of this paper.

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Section: Introductionmentioning

confidence: 99%

New stability criteria for stochastic perturbed singular systems in mean square

2021

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“…In a complex environment, disturbances of system include measured noise, external environment disturbance, change of the system structure and modeling error (Han et al, 2018; Hu et al, 2019; Jiao et al, 2019; Wei and Sun, 2018; Zhang et al, 2015). Since various types of disturbances always effect the control accuracy of the system, the problem of anti-disturbance control for systems with multiple disturbances has been a hot topic in the control field (Liu et al, 2018; Sun et al, 2018; Wei et al, 2019, 2016).…”

Section: Introductionmentioning

confidence: 99%

Elegant anti-disturbance control for stochastic systems with multiple heterogeneous disturbances based on fuzzy logic systems

You

Wei

Han

et al. 2020

Transactions of the Institute of Measurement and Control

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There are a large number of non-harmonic disturbances generated by nonlinear exogenous systems in realistic engineering. The current disturbance observer is not applicable for estimating the non-harmonic disturbance with unknown nonlinear dynamics, thus greatly reducing the accuracy of the controller. This paper addresses a class of stochastic systems with multiple heterogeneous disturbances including white noise and non-harmonic disturbance with unknown smooth nonlinear function, which can be approximated by fuzzy logic systems. Based on the approximation of the unknown nonlinear function, an adaptive disturbance observer (ADO) is constructed to estimate non-harmonic disturbance. Combining disturbance observer-based control with fuzzy control, an elegant anti-disturbance control (EADC) scheme is proposed such that the composite system achieves asymptotically bounded in mean square. Simulation examples show that the state responses of the system gradually approache [Formula: see text] from divergence, indicating that the effectiveness of the controller is satisfactory. In addition, the anti-disturbance control accuracy of EADC approximately improves [Formula: see text] times compared with [Formula: see text] control. The simulation results demonstrate the feasibility and effectiveness of the proposed scheme.

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Input‐to‐state stability of impulsive stochastic systems with state‐dependent impulses and regime‐switching

Kuang,

Gao,

2024

Intl J Robust & Nonlinear

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This article introduces a unified criterion for input‐to‐state stability (ISS), integral input‐to‐state stability (iISS) and ‐input‐to‐state stability (‐ISS) of impulsive stochastic system with switching. The criterion demonstrates that the premise of a switching‐impulse system to achieve three types of ISS is that a mutually constraining relationship between switching, impulse and continuous dynamics needs to be satisfied. Furthermore, using it we know that switching can stabilize a system containing stabilizing factors by affecting both continuous dynamics and impulses, that switching itself is one of the factors in system instability, and that impulses have a dual effect on the stability of the system. The coefficients of the upper bound of Lyapunov functional differential operators are time‐varying functions and the impulses contain stable and unstable impulses, including the case of constants, which advances and improves the existing results. Finally, an example and its simulation results are given to verify the validity of theoretical analysis.

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Stability criteria of stochastic nonlinear systems with asynchronous impulses and switchings

Cited by 19 publications

References 33 publications

New stability criteria for stochastic perturbed singular systems in mean square

New stability criteria for stochastic perturbed singular systems in mean square

Elegant anti-disturbance control for stochastic systems with multiple heterogeneous disturbances based on fuzzy logic systems

Input‐to‐state stability of impulsive stochastic systems with state‐dependent impulses and regime‐switching

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