Fault Detection Filter Design of Polytopic Uncertain Continuous-Time Singular Markovian Jump Systems with Time-Varying Delays

This paper investigates the problem of full-order and reduced-order fault detection filter (FDF) design under unified linear matrix inequality (LMI) conditions for a class of continuous-time singular Markovian jump systems (CTSMJSs) with time-varying delays and polytopic uncertain transition rates. By constructing a new Lyapunov function, sufficient conditions are firstly provided for the singular model error augmented system such that the system is stochastically admissible with an H∞ performance level γ. And then, by applying a novel convex polyhedron technique to decoupled linear matrix inequalities, the full-order and reduced-order fault detection filter parameters can be obtained within a convex optimization frame. The reduced-order fault detection filter (FDF) can not only meet the fault detection accuracy requirements of complex systems but also improve the fault detection efficiency. Finally, a DC motor and an illustrative simulation example are given to verify the feasibility and effectiveness of the proposed algorithms.

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A Reduced-order Fault Detection Filter Design for Polytopic Uncertain Continuous-time Markovian Jump Systems with Time-varying Delays

International Journal of Control Automation and Systems ◽

10.1007/s12555-017-0182-3 ◽

2018 ◽

Vol 16 (5) ◽

pp. 2021-2032 ◽

Cited By ~ 8

Author(s):

Lihong Rong ◽

Xiuyan Peng ◽

Biao Zhang

Keyword(s):

Fault Detection ◽

Continuous Time ◽

Filter Design ◽

Markovian Jump Systems ◽

Time Varying ◽

Markovian Jump ◽

Reduced Order ◽

Fault Detection Filter ◽

Jump Systems ◽

Detection Filter

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Robust non-fragile H∞ fault detection filter design for delayed singular Markovian jump systems with linear fractional parametric uncertainties

Nonlinear Analysis Hybrid Systems ◽

10.1016/j.nahs.2018.11.001 ◽

2019 ◽

Vol 32 ◽

pp. 65-78 ◽

Cited By ~ 16

Author(s):

Guobao Liu ◽

Ju H. Park ◽

Shengyuan Xu ◽

Guangming Zhuang

Keyword(s):

Fault Detection ◽

Filter Design ◽

Markovian Jump Systems ◽

Parametric Uncertainties ◽

Markovian Jump ◽

Fault Detection Filter ◽

Singular Markovian Jump Systems ◽

Jump Systems ◽

Detection Filter

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Fault detection filter design for continuous-time nonlinear Markovian jump systems with mode-dependent delay and time-varying transition probabilities

Advances in Difference Equations ◽

10.1186/s13662-017-1313-0 ◽

2017 ◽

Vol 2017 (1) ◽

Cited By ~ 5

Author(s):

B Wang ◽

FC Zou ◽

J Cheng ◽

SM Zhong

Keyword(s):

Fault Detection ◽

Continuous Time ◽

Filter Design ◽

Transition Probabilities ◽

Markovian Jump Systems ◽

Time Varying ◽

Markovian Jump ◽

Jump Systems ◽

Nonlinear Markovian Jump Systems ◽

Detection Filter

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Improved Reduced-Order Fault Detection Filter Design for Polytopic Uncertain Discrete-Time Markovian Jump Systems with Time-Varying Delays

Complexity ◽

10.1155/2018/9489620 ◽

2018 ◽

Vol 2018 ◽

pp. 1-15 ◽

Cited By ~ 4

Author(s):

Lihong Rong ◽

Xiuyan Peng ◽

Liangliang Liu ◽

Biao Zhang

Keyword(s):

Fault Detection ◽

Discrete Time ◽

Filter Design ◽

Sufficient Conditions ◽

Time Varying ◽

Markovian Jump ◽

Reduced Order ◽

Fault Detection Filter ◽

Markovian Jump Linear Systems ◽

Detection Filter

The fault detection (FD) reduced-order filtering problem is investigated for a family of polytopic uncertain discrete-time Markovian jump linear systems (MJLSs) with time-varying delays. Under meeting the control precision requirements of the complex systems, the reduced-order fault detection filter can improve the efficiency of the fault detection. Then, by the aid of the Markovian Lyapunov function and convex polyhedron techniques, some novel time-varying delays and polytopic uncertain sufficient conditions in terms of linear matrix inequality (LMI) are proposed to insure the existence of the FD reduced-order filter. Finally, an illustrative example is provided to verify the usefulness of the given method.

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H∞ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties

ISA Transactions ◽

10.1016/j.isatra.2014.05.021 ◽

2014 ◽

Vol 53 (4) ◽

pp. 1024-1034 ◽

Cited By ~ 27

Author(s):

Guangming Zhuang ◽

Jianwei Xia ◽

Yuming Chu ◽

Fu Chen

Keyword(s):

Fault Detection ◽

Filter Design ◽

Markovian Jump Systems ◽

Time Varying ◽

Markovian Jump ◽

Parameter Uncertainties ◽

Fault Detection Filter ◽

Jump Systems ◽

Detection Filter

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A Reduced-Order Fault Detection Filtering Approach for Continuous-Time Markovian Jump Systems with Polytopic Uncertainties

Complexity ◽

10.1155/2017/4927453 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 4

Author(s):

Lihong Rong ◽

Xiuyan Peng ◽

Biao Zhang

Keyword(s):

Fault Detection ◽

Continuous Time ◽

External Disturbance ◽

Linear Matrix ◽

Transition Rates ◽

Markovian Jump ◽

Reduced Order ◽

Order Filter ◽

Markovian Jump Linear Systems ◽

Jump Systems

The fault detection (FD) reduced-order filtering problem is investigated for a family of continuous-time Markovian jump linear systems (MJLSs) with polytopic uncertain transition rates, which also include the totally known and partly unknown transition rates. Then, in accordance with the convexification techniques, a novel sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained in terms of linear matrix inequality (LMI), which can ensure the error augmented system with the FD reduced-order filter is randomly 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, the effectiveness of the proposed method is substantiated with two illustrative examples.

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