Robust fault detection and estimation for descriptor systems based on multi-models concept

  • Habib Hamdi
  • Mickael RodriguesEmail author
  • Chokri Mechmeche
  • Naceur Benhadj Braiek
Technical Notes and Correspondence Intelligent and Information Systems


This paper addresses the robust fault detection and estimation problem of nonlinear descriptor system with unknown inputs observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. Two cases are considered: the first one deals with the multi-models based on measurable decision variables and the second one assumes that these decision variables are unmeasurable. Then, a residual generator based on an unknown observer is designed for both fault detection and estimation. Stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs) for both cases. The performances of the proposed fault detection and estimation method is successfully applied to an electrical circuit.


Descriptor multi-models fault detection and estimation Linear Matrices Inequalities (LMIs) residual generation 


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  1. [1]
    G. D. A. T. Vemuri, M. M. Polycarpou, and A. R. Ciric, “Fault diagnosis of differential-algebraic systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 31, no. 2, pp. 143–152, March 2001.CrossRefGoogle Scholar
  2. [2]
    D. Koenig, “Observer design for unknown input nonlinear descriptor systems via convex optimization,” IEEE Trans. on Automatic Control, vol. 51, no. 6, pp. 1047–1052, June 2006.MathSciNetCrossRefGoogle Scholar
  3. [3]
    H. Hamdi, M. Rodrigues, C. Mechmeche, D. Theilliol, and N. BenHadj Braiek, “Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer,” International Journal of Adaptive Control and Signal Processing, vol. 26, pp. 224–240, 2012.MathSciNetCrossRefGoogle Scholar
  4. [4]
    J. L. Chen, “Robust ESPR analysis and control for uncertain continuous-time descriptor systems,” International Journal of Control, Automation, and Systems, vol. 8, no. 1, pp. 8–15, 2010.CrossRefGoogle Scholar
  5. [5]
    J. Sjoberg, “Some results on optimal control for non-linear descriptor systems,” Sweden Studies in Science and Technology, Thesis No. 1227, 2006.Google Scholar
  6. [6]
    M. Darouach and M. Boutayeb, “Design of observers for descriptor systems,” IEEE Trans. on Automatic Control, vol. 40. no. 7, pp. 1323–1327, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    M. Rodrigues, D. Theilliol, M. Adam-Medina, and D. Sauter, “A fault detection and isolation scheme for industrial systems based on multiple operating models,” Control Engineering Practice, vol. 16, pp. 225–239, 2008.CrossRefGoogle Scholar
  8. [8]
    T. Taniguchi, K. Tanaka, and H. O. Wang, “Fuzzy descriptor systems and nonlinear model following control,” IEEE Trans. on Fuzzy Systems, vol. 8, no. 4, pp. 442–452, August 2000.CrossRefGoogle Scholar
  9. [9]
    Y. Wang, Z. Q. Sun, and F. C. Sun, “Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 2, no. 1, pp. 76–82, March 2004.Google Scholar
  10. [10]
    Z. Gao and S. X. Ding, “Fault reconstruction for Lipschitz nonlinear descriptor systems via linear matrix inequality approach” Circuits Syst. Signal Process, vol. 27, pp. 295–308, 2008.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Z. Gao and S. X. Ding, “Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems” Automatica, vol. 43, pp. 912–920, 2007.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Habib Hamdi
    • 1
  • Mickael Rodrigues
    • 2
    Email author
  • Chokri Mechmeche
    • 1
  • Naceur Benhadj Braiek
    • 1
  1. 1.Laboratory for Advanced Systems (LSA)Polytechnic School of TunisiaTunisTunisia
  2. 2.Laboratory Automation and Engineering Process (LAGEP), CNRS UMR 5007University Lyon1Lyon1France

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