Asymptotic stability in probability for discrete‐time stochastic coupled systems on networks with multiple dispersal

Wang, Pengfei; Hong, Yu; Su, Huan

doi:10.1002/rnc.3927

Cited by 15 publications

(2 citation statements)

References 49 publications

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“…It can be found from (1) that the process disturbance (t) has a great influence to system state x(t). In most existing literatures, 17,[48][49][50] the intensity of the disturbance has a lower level than system state. Namely, the magnitude of each entry in D (t) is always less than that of system state Ax(t).…”

Section: Preliminariesmentioning

confidence: 99%

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

Cui

2019

Intl J Robust & Nonlinear

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This paper concerns the controller design for continuous-time linear systems with time-varying delay and process disturbance. A novel adaptive sliding mode control law is mainly proposed to attract the sliding mode to first-order sliding surface within a finite time; afterwards, the uniformly ultimately bounded stability of the closed-loop system on the sliding surface is simultaneously guaranteed. In addition, the chattering phenomena can be conveniently excluded if the disturbance is a low-intensity process. Once the high-intensity disturbance is involved, the state variation can be significantly reduced as well. Furthermore, by the technique of a novel exponential free-matrix technique, the convergence rate of the closed-loop system can be conveniently preregulated. Numerical example is provided to demonstrate the effectiveness of the proposed method. KEYWORDSadaptive sliding mode control, chattering free, process disturbance, time-varying delay, uniformly ultimately bounded stable INTRODUCTIONMany real-world applications are difficult to be accurately described by the mathematical models because their full-scale intrinsic and extrinsic dynamics are usually hard or even barely impossible to be acquired. The practical systems usually contain some unclear system variations including mismatches between idealized model with the reality, unmodeled system dynamic, unknown operating mechanism, etc. If these system variations are completely neglected, the system control performances will be deteriorated; moreover, the system stability may be threatened. For describing the unknown and unmeasurable variations, the process disturbances are usually employed in the system dynamic models. [1][2][3][4][5] Although the detailed origination and transmutation dynamics of process disturbances still remain unrevealed, some statistical models are successful to describe their macroscopically principles. For example, the disturbances are regarded as the stochastic distributions, 6,7 the energy-bounded processes, 8-11 the peak-bounded procedures, 12-14 etc. For alleviating the negative impacts of the process disturbances, many robust control schemes are gradually proposed in the past decades. [15][16][17][18][19][20] One of the successful robust control scheme is called the sliding mode control (SMC), also known as the variable structure control, which received intensive attentions due to its prominent features such as convenient to be performed, easy implementation, insensitivity to dynamic switching of system modes, reduction of the order of system state, and especially the robustness in the presence of external disturbances. [21][22][23][24] Int J Robust Nonlinear Control. 2019;29:3389-3404.wileyonlinelibrary.com/journal/rnc

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Section: Preliminariesmentioning

confidence: 99%

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

Cui

2019

Intl J Robust & Nonlinear

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“…It has been regarded as a powerful method for stability analysis and stabilization of CSNs. Some works have reported on the basis of this method . However, to our best knowledge, there are few other researchers who have used the approach in which the Lyapunov method and Kirchhoff's Matrix Tree Theorem are combined to investigate finite‐time stability and the relevant stabilization.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Liu

2018

Asian Journal of Control

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In this paper, finite-time stabilization of coupled systems on networks with time-varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self-delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite-time stabilization of coupled oscillators with time-varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.

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Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

Wang

2018

Nonlinear Dyn

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Asymptotic stability in probability for discrete‐time stochastic coupled systems on networks with multiple dispersal

Cited by 15 publications

References 49 publications

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

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