Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion

Khandani, Khosro; Majd, Vahid Johari; Tahmasebi, Mahdieh

doi:10.1080/00207721.2016.1216201

Cited by 30 publications

(28 citation statements)

References 40 publications

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“…FBMs now have been extensively used to model the stochastic perturbations as the input noise in dynamical systems. [13][14][15][16][17][18][19] For example, the integral sliding mode control for uncertain stochastic time-delay systems driven by FBMs was considered and a Lyapunov function with exponential term was proposed in Reference 14. Then the criterion of stochastic stability proposed in Reference 14 was not related to the Hurst index of FBMs.…”

Section: Introductionmentioning

confidence: 99%

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

Xie

Meng

Kao

et al. 2021

Intl J Robust & Nonlinear

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The quantized feedback control for a type of delayed Markovian jumping singular systems driven by fractional Brownian motions is investigated. Firstly, the input is quantized by a uniform operator consisting of a linear part to deal with system stochastic stability and a nonlinear part to deal with the error caused by the quantizer. Secondly, to deal with the boundedness of fractional Brownian motions, a new type of Lyapunov function dependent of Hurst index is constructed. Then, utilizing generalized Finsler lemma and Gronwall inequality, some new criteria on the singular stochastic finite-time boundedness are obtained for the considered systems with the designed quantized input. Finally, a numerical example and a DC motor example are presented to verify the effectiveness of the proposed methods and results.

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Section: Introductionmentioning

confidence: 99%

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

Xie

Meng

Kao

et al. 2021

Intl J Robust & Nonlinear

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“…Stability and stabilization of MJSs (Ali et al, 2019), ﬁltering (Li and Wang, 2012; Peng et al, 2019), and controller design for MJSs (Fei et al, 2017; Hou and Sun, 2018; Ma et al, 2018) have been well addressed in the literature. In recent years, SMC as a powerful robust method has been applied to different classes of fractional-order systems such as time-delay fractional order systems (Yousefi and Binazadeh, 2018), fractional-order chaotic systems (Roohi et al, 2019), fractional stochastic systems (Khandani et al, 2016, 2017) and so on. SMC has also been widely applied to MJSs; see Chen et al (2011), Jiang et al (2019), Kao et al (2014), Shen et al (2018), Zhang et al (2012), Zhao et al (2019) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

Parvizian

Khandani

Majd

2020

Transactions of the Institute of Measurement and Control

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In this paper, state estimation and adaptive sliding mode control (SMC) of uncertain fractional-order Markovian jump systems (FO-MJSs) with time delay and input nonlinearity are considered. A non-fragile observer is proposed to estimate the system states, and an observer-based adaptive sliding mode controller is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space in finite time. The sufficient condition for stochastic stability of the error system and sliding mode dynamics is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method.

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“…MJSs have been well investigated formerly, and the results on their stabilization, filtering and controller design are available. 1–7 Particularly, one popular control strategy is sliding mode control (SMC) which is a powerful robust method with many applications in various systems, 8–11 and has been extensively employed in the literature for MJSs. 12–14 For instance, in Xu et al, 15 an adaptive SMC strategy based on an integral type sliding surface has been proposed to investigate the stability of a Markovian jump model with parameter uncertainties, nonlinearities and Lévy noises.…”

Section: Introductionmentioning

confidence: 99%

A diffusive representation approach toward H_∞ sliding mode control design for fractional-order Markovian jump systems

Parvizian

Khandani

2020

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article proposes a new [Formula: see text] sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov–Krasovskii functional, the problem of [Formula: see text] sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given [Formula: see text] disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.

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Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion

Cited by 30 publications

References 40 publications

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

A diffusive representation approach toward H_∞ sliding mode control design for fractional-order Markovian jump systems

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Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion

Cited by 30 publications

References 40 publications

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

A diffusive representation approach toward H∞ sliding mode control design for fractional-order Markovian jump systems

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A diffusive representation approach toward H_∞ sliding mode control design for fractional-order Markovian jump systems