Fault detection for Markovian jump systems

Zhong, Maiying; Ye, H; Shi, Peng; Wang, G

doi:10.1049/ip-cta:20045085

Cited by 166 publications

(134 citation statements)

References 11 publications

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“…Let γ > 0 be a given scalar; if there are positive-definite symmetric matrices P = {P 1 , P 2 , ...P N } such that LMI (8) holds, then the error augmented system in (5) with deficient transition information is randomly stable with a guaranteed H ∞ performance index γ and satisfies (6).…”

Section: Lemmamentioning

confidence: 99%

“…Many important results have been reported, such as a number of studies on the Markovian jump system on the filter design [3][4][5], controller design [6], output feedback control [7][8][9][10], stability analysis and synthesis [11][12][13]. In fact, MJLSs are very appropriate to dynamical model systems whose property is subject to random sudden variant due to abrupt external disturbance, shifting of the action spots of a nonlinear system, and repairs of components, thus, in order to ensure the nonlinear system stochastically exponentially stable, the author in [9] proposed a Markovian Lyapunov functional which was been successfully used in the nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

Rong

Peng

Zhang

2016

EURASIP J. Adv. Signal Process.

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The paper addresses the fault detection (FD) problem for a class of discrete-time Markov jump linear systems (MJLSs) with deficient transition rates, which simultaneously considers the totally known, partly unknown, and uncertain transition rates. Then, in accordance with the linear matrix inequality (LMI) method and the convexification techniques, a sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained, which can ensure the error augmented system with the FD reduced-order filter is stochastically stable. In addition, a performance index is given to enhance the robustness of the residual system against deficient transition information and external disturbance, such that the error between the fault and the residual is made as small as possible to reinforce the faults sensitivity. Finally, an illustrative example is employed to show the effectiveness of the proposed design approach.

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Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

Rong

Peng

Zhang

2016

EURASIP J. Adv. Signal Process.

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“…More recently, a few achievements have been published in the literature [10,14,17,18]. In [17], an observer-based residual generator has been designed by solving a two-objective optimization problem; in [14] and [18], the problems of observer-based fault detection are considered in the framework of H ∞ -filtering formulation; in [10], a networked control system was modelled by a discrete-time Markovian jump system and the problem of H ∞ fault detection filter was designed. To the best of authors' knowledge, however, the problem of parity space-based fault detection for Markovian jump systems has not been fully investigated yet, which motivates us for the present study.…”

Section: Introductionmentioning

confidence: 99%

Parity space-based fault detection for Markovian jump systems

Zhong¹,

Ding²,

Shi³

2009

International Journal of Systems Science

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Abstract. This paper deals with problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems. A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices. Different from the case of linear time invariant systems, the parity space-based residual generator for a Markovian jump system cannot be designed off-line because it depends on the history of system modes in the last finite steps. In order to overcome this difficulty, a finite set of parity matrices is pre-designed applying a unified approach to linear time invariant systems. Then the on-line residual generation can be easily implemented. Moreover, the problem of residual evaluation is also considered which includes the determination of a residual evaluation function and a threshold. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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“…Therefore, it is of great significance to design a robust FDI system [7]- [10]. Recently, an H∞-filtering formulation of FDI problem has been presented to solve the robust FDI problem [11]- [13]. In [11], the problem of Robust Fault Detection Filter Design (RFDFD) for discrete-time Markovain jump linear systems is formulated as an H∞-filtering problem.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, an H∞-filtering formulation of FDI problem has been presented to solve the robust FDI problem [11]- [13]. In [11], the problem of Robust Fault Detection Filter Design (RFDFD) for discrete-time Markovain jump linear systems is formulated as an H∞-filtering problem. In [13], the problem of RFDFD for discrete-time networked systems with multiple state delays and unknown input is transformed into an H∞-filtering problem for Markovain jumping system.…”

Section: Introductionmentioning

confidence: 99%

Robust Fault Detection for Switched Linear Systems With State Delays

Wang

Shi

2009

IEEE Trans. Syst., Man, Cybern. B

250

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Abstract-This paper deals with the problem of robust fault detection for discrete-time switched systems with state delays under arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs and model uncertainties, the estimation error between the residuals and the faults is minimized. The problem of robust fault detection is converted into an H∞ filtering problem. By switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed method.

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Fault detection for Markovian jump systems

Cited by 166 publications

References 11 publications

Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

Parity space-based fault detection for Markovian jump systems

Robust Fault Detection for Switched Linear Systems With State Delays

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