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

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
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.

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

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Reduced Order ◽  
Fault Detection Filter ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Detection Filter

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.

Full- and Reduced-Order Fault Detection Filter Design With Application in Flow Transmission Lines

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Saeed Salavati ◽  
Karolos Grigoriadis ◽  
Matthew Franchek ◽  
Reza Tafreshi
Keyword(s):  
Fault Diagnosis ◽  
Fault Detection ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Fault Detection And Isolation ◽  
Linear Matrix ◽  
Reduced Order ◽  
Fault Detection Filter ◽  
Order Filter ◽  
Detection Filter

The full- and reduced-order fault detection filter design is examined for fault diagnosis in linear time-invariant (LTI) systems in the presence of noise and disturbances. The fault detection filter design problem is formulated as an H∞ problem using a linear fractional transformation (LFT) framework and the solution is based on the bounded real lemma (BRL). Necessary and sufficient conditions for the existence of the fault detection filter are presented in the form of linear matrix inequalities (LMIs) resulting in a convex problem for the full-order filter design and a rank-constrained nonconvex problem for the reduced-order filter design. By minimizing the sensitivity of the filter residuals to noise and disturbances, the fault detection objective is fulfilled. A reference model can be incorporated in the design in order to shape the desired performance of the fault detection filter. The proposed fault detection and isolation (FDI) framework is applied to detect instrumentation and sensor faults in fluid transmission and pipeline systems. To this end, a lumped parameter framework for modeling infinite-dimensional fluid transient systems is utilized and a low-order model is obtained to pursue the instrumentation fault diagnosis objective. Full- and reduced-order filters are designed for sensor FDI. Simulations are conducted to assess the effectiveness of the proposed fault detection approach.

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