Robust ${\mathscr H}_{\infty }$ Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme

Gao, Qing; Feng, Gang; Xi, Zhiyu; Wang, Yong; Qiu, Jianbin

doi:10.1109/tfuzz.2013.2256914

Cited by 76 publications

(36 citation statements)

References 16 publications

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“…It shows that system (29) achieves the mean-square H ∞ performance under observer-based boundary controller (31).…”

Section: Examplementioning

confidence: 95%

“…Indeed, the problem of H ∞ control has been studied by many. [31][32][33][34][35][36] However, few results exist for H ∞ observer-based boundary control for SRDSs.…”

Section: Introductionmentioning

confidence: 99%

“…H ∞ control is known to be an effective control strategy to handle disturbance effects. Indeed, the problem of H ∞ control has been studied by many . However, few results exist for H ∞ observer‐based boundary control for SRDSs.…”

Section: Introductionmentioning

confidence: 99%

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Boundary control of linear stochastic reaction‐diffusion systems

Liu

Shi

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper considers the boundary control problem for linear stochastic reaction‐diffusion systems with Neumann boundary conditions. First, when the full‐domain system states are accessible, a boundary control is designed, and a sufficient condition is established to ensure the mean‐square exponential stability of the resulting closed‐loop system. Next, when the full‐domain system states are not available, an observer‐based control is proposed such that the underlying closed‐loop system is stable. Furthermore, observer‐based controller is designed for the systems with an H∞ performance. Simulation examples are given to demonstrate the effectiveness and potential of the new design techniques.

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“…It shows that system (29) achieves the mean-square H ∞ performance under observer-based boundary controller (31).…”

Section: Examplementioning

confidence: 95%

“…Indeed, the problem of H ∞ control has been studied by many. [31][32][33][34][35][36] However, few results exist for H ∞ observer-based boundary control for SRDSs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boundary control of linear stochastic reaction‐diffusion systems

Liu

Shi

et al. 2018

Intl J Robust & Nonlinear

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“…This constraint condition restricts the technique to be applied. This problem has been solved for regular T–S fuzzy systems [42]. However, to the authors' best knowledge, in the current literature, few effective results on removing the constraint assumption for the T–S fuzzy descriptor systems with SMC [43] have been obtained, which is the first motivation to study.…”

Section: Introductionmentioning

confidence: 99%

Robust stabilisation for a class of stochastic T–S fuzzy descriptor systems via dynamic sliding‐mode control

Shi

Zhang

2020

IET Control Theory & Applications

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“…As one of the most useful robust control techniques in classical engineering, H 1 control has been extensively studied and widely used in classical feedback control systems [16][17][18][19][20][21]. The most promising feature of H 1 control is the guaranteed stability margin it provides against norm bounded perturbations [22,23].…”

Section: Introductionmentioning

confidence: 99%

Robust H ^∞ controller design for a class of linear quantum systems with time delay

Wang

Gao

Dong

2016

Int. J. Robust. Nonlinear Control

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Time delay is frequently encountered in practical quantum feedback control systems with long transmission lines and measurement process. This paper is concerned with measurement-based feedback H 1 control for quantum systems with time delays appearing in the feedback loops. A physical model is presented for the quantum time-delay system described by complex quantum stochastic differential equations. Quantum versions of some fundamental properties, such as dissipativity and stability, are discussed for this model. A numerical procedure is proposed for H 1 controller synthesis, which can deal with a non-convex optimization problem arising in the design processes.ROBUST H 1 CONTROLLER DESIGN FOR LINEAR QUANTUM SYSTEMS WITH TIME DELAY 381 controller synthesis for a class of linear quantum stochastic systems has been formulated and solved. Reference [24] presented an experimental realization of a coherent quantum feedback control system using H 1 control theory. In Reference [25], an H 1 control problem has been considered for a class of linear quantum systems with time delays described by position and momentum quadratures for the quantum system variables.In this paper, H 1 control of a class of quantum time-delay systems is investigated, where the systems are described by complex quantum stochastic differential equations (QSDEs) in terms of annihilation and creation operators. The representation of complex QSDEs is a natural description for a class of widely used quantum optical systems [12,26,27]. In this paper, we call the quantum system described by complex QSDEs a complex quantum system [12,26]. The system under consideration is a mixed quantum-classical system in the sense that the plant is quantum while the controller is classical. Relations between the complex QSDEs under consideration and the corresponding real QSDEs defined in terms of quadrature variables are presented. The performance properties of the proposed model such as stability and dissipativity are also derived and characterized in complex algebraic terms, which leads to a complex quantum version of the bounded real lemma. It is found that controller synthesis suffers from several limitations because of the nonlinear and non-convex constraints and many decision variables involved in design procedures. To conquer these limitations, a numerical procedure is developed for H 1 controller design.The rest of the paper is organized as follows. Section 2 gives a brief overview of quantum systems with real quadrature representation and annihilation-creation operator representation, respectively, and presents a connection between them. Section 3 presents the setup of the closed loop system with time delay. Section 4 investigates performance characteristics such as dissipativity and stability for the model given in Section 3. Section 5 presents the H 1 controller synthesis for the proposed model, which is verified by a numerical example. Section 6 concludes this paper.

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Robust ${\mathscr H}_{\infty }$ Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme

Cited by 76 publications

References 16 publications

Boundary control of linear stochastic reaction‐diffusion systems

Boundary control of linear stochastic reaction‐diffusion systems

Robust stabilisation for a class of stochastic T–S fuzzy descriptor systems via dynamic sliding‐mode control

Robust H ^∞ controller design for a class of linear quantum systems with time delay

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Robust ${\mathscr H}_{\infty }$ Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme

Cited by 76 publications

References 16 publications

Boundary control of linear stochastic reaction‐diffusion systems

Boundary control of linear stochastic reaction‐diffusion systems

Robust stabilisation for a class of stochastic T–S fuzzy descriptor systems via dynamic sliding‐mode control

Robust H ∞ controller design for a class of linear quantum systems with time delay

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Robust H ^∞ controller design for a class of linear quantum systems with time delay