State Space Solution to the H-/H∞ Fault Detection Problem

In this paper we give a state space solution to the H<sub>-</sub>/H<sub>∞</sub> fault detection (FD) problem for linear time invariant dynamic systems. An H<sub>-</sub>/H<sub>∞</sub> FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state space realization of the optimal filter in an observer form via the solution of linear matrix inequalities (LMIs). A numerical example is given to illustrate the algorithm

[1]  Paul M. Frank,et al.  An Approach to Residual Generator and Evaluator Design and Synthesis , 1993 .

[2]  James Lam,et al.  An LMI approach to design robust fault detection filter for uncertain LTI systems , 2003, Autom..

[3]  Ákos László.  A generalization of the bounded real lemma , 2003 .

[4]  Richard Vernon Beard,et al.  Failure accomodation in linear systems through self-reorganization. , 1971 .

[5]  Dominique Sauter,et al.  Optimal thresholding for robust fault detection of uncertain systems , 2000 .

[6]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[7]  P. Frank,et al.  Fault detection via factorization approach , 1990 .

[8]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[9]  X. Steven Ding,et al.  Current Developments in the Theory of FDI , 2000 .

[10]  Paul M. Frank,et al.  A frequency domain approach to fault detection of uncertain dynamic systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[11]  Kemin Zhou,et al.  Performance bounds for coprime factor controller reductions , 1995 .

[12]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[13]  Henrik Niemann,et al.  Norm based design of fault detectors , 1999 .

[14]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[15]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results , 1990, Autom..

[16]  R. J. Patton,et al.  On Sensitivity of Robust Fault Detection Observers , 1999 .

[17]  Steven X. Ding,et al.  Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis , 1994, Autom..

[18]  Steven X. Ding,et al.  Current development in the theory of FDI , 2000 .