Fault Diagnosability Analysis of Two-Dimensional Linear Discrete Systems

Zhao, Dong; Ahn, Choon Ki; Paszke, Wojciech; Fu, Fangzhou; Li, Yueyang

doi:10.1109/tac.2020.2986054

Cited by 25 publications

(6 citation statements)

References 29 publications

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“…We use V i (i ∈ N ) and the fuzzy function α i (t, k) to construct V (α) := N i=1 α i (t, k)V i . Thus, together with (3) and (31), conditions (32) and ( 33) are guaranteed by (40) and (41), respectively. The proof is completed by virtue of Theorem 3.4.…”

Section: Numerical Example Consider the Following Nonlinear Continuou...mentioning

confidence: 87%

“…The signals or variables of 2-D systems are dependent on two independent variables, that could be both continuous or both discrete or mixed continuous-discrete. The existing research has been devoted mainly toward 2-D discrete systems because of their wide range of applications, and they are comparatively easy to be investigated by modern mathematical tools [33,40,34,20]. Compared to the fruitful results of 2-D discrete systems, analysis on the continuous-discrete systems are less reported in relative publications.…”

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confidence: 99%

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$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

Duan

Liang

Xiang

2022

DCDS-S

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<p style='text-indent:20px;'>In this paper, the <inline-formula><tex-math id="M2">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An <inline-formula><tex-math id="M3">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard <inline-formula><tex-math id="M4">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF <inline-formula><tex-math id="M5">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance. A numerical tractable method for designing a controller is obtained through matrixing, thus giving conveniently the expression of controller with linear matrix inequality as tool kit.</p>

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Section: Numerical Example Consider the Following Nonlinear Continuou...mentioning

confidence: 87%

mentioning

confidence: 99%

$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

Duan

Liang

Xiang

2022

DCDS-S

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“…The effectiveness of the proposed estimator is illustrated by applying two numerical examples. Extending the developed filtering strategy for 2-D dynamical linear and nonlinear systems with the adaptive event-triggered mechanism, 38 fault, 17,44 and considering more imperfections in the communication medium, such as transmission delay 34,45 and cyber-attack 46 define our future research line.…”

Section: Discussionmentioning

confidence: 99%

Scalable recursive state estimation for nonlinear two‐dimensional complex networks with switching topology

Rezaei

Farnam

Crevecoeur

2023

Intl J Robust & Nonlinear

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This paper investigates a scalable recursive state estimation method for nonlinear two-dimensional (2-D) stochastic complex networks. In these networks, the switching topology is modelled by random variables generated by the Bernoulli distribution. Considering the Extended Kalman Filter structure, we employ the Taylor series expansion to handle the nonlinear functions in the model. Hence, high-order terms emerging in the linearization process are modelled by norm-bounded parameter uncertainties. Due to the uncertainty of such a system, we obtain an upper bound for the estimation error covariance. Furthermore, we obtain an upper bound for the cross covariance to reduce the proposed filter's computational complexity and improve scalability. Within the established setting, next, the proposed filter is designed in such a way that the presented upper bounds are minimized. Finally, a numerical example is provided to illustrate the effectiveness of the proposed state estimation algorithm.

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“…With the aid of Proposition 1 and the analysis above, we turn our attention to (14) subject to the quasi-linear dynamics (11), rather than directly solving the original H ∞ FE problem via optimizing performance index (9) subject to the uncertain nonlinear model (8). Therefore, by defining…”

Section: Proof Please See Appendix a ▪mentioning

confidence: 99%

“…Since a model of a plant always involves mismatched terms, such as modeling uncertainties, disturbances, noises, and/or component changes, to effectively identify a fault, suppression should be inflicted on these terms, while excitation should be put on the fault signal. [1][2][3][4][5][6][7][8][9][10] If an engineer not only aims to detect a fault but also excavate its magnitude online, fault estimation (FE) serves as a significant role in delivering the shape and the occurrence time of a fault. For achieving satisfactory FE, some optimization methodologies in both H ∞ and H 2 senses are widely employed.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered fault estimation for discrete time‐varying systems subject to sector‐bounded nonlinearity: A Krein space based approach

Liu

Zhao

et al. 2021

Intl J Robust & Nonlinear

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In this study, event‐triggered fault estimation (FE) problem for a class of discrete‐time dynamic systems subject to sector‐bounded nonlinearity and time‐varying coefficients is investigated. For a given event‐triggered measurement transmission scheme, the event‐induced output non‐persistence for the fault estimator is modeled by norm‐bounded observation uncertainty. After giving a suitable H∞ performance index and formulating the estimation problem for the concerned nonlinear system with event‐triggered measurements, an auxiliary model in a quasi‐linear form and an associated H∞ performance function are established. With the aid of this auxiliary model and performance function, the sector‐bounded nonlinearity condition and the induced observation uncertainty are packaged simultaneously, and the considered H∞ FE problem in Hilbert space is recast as an H2 deconvolution filtering issue in Krein space. Through designing Krein space based model with appropriate inner products, and using the orthogonally projection technique, fault estimator is derived in an analytical and recursive manner. The condition that ensures the existence of the estimator is also obtained. Two examples are adopted to demonstrate the applicability of the proposed method.

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Fault Diagnosability Analysis of Two-Dimensional Linear Discrete Systems

Cited by 25 publications

References 29 publications

$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

Scalable recursive state estimation for nonlinear two‐dimensional complex networks with switching topology

Event‐triggered fault estimation for discrete time‐varying systems subject to sector‐bounded nonlinearity: A Krein space based approach

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