Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems


This paper focuses on the problem of fault estimation for a class of interconnected nonlinear systems with time varying delays. In contrast to the common assumption imposed on the problem in most literature, here, there is no need for the delay rate to be less than one. Both actuator and component faults are considered within the general fault model invoked as multiplicative faults in this study. Robust adaptive observers are used to detect and estimate simultaneously the states and the parameter faults in each subsystem. The designed observers ensure a prescribed H performance level for the fault estimation error, irrespective of the uncertainties which are assumed here to be the unknown interconnections between the subsystems. With the aid of H performance index, the common assumption regarding the observer matching condition is no longer required. Sufficient conditions for asymptotic stability of the observers are derived via a matrix inequality approach with the aid of LyapunovKrasovskii function. Finally, a simulation example is presented to show the validity and feasibility of the proposed method.

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Author information



Corresponding author

Correspondence to Alireza Khayatian.

Additional information

Recommended by Associate Editor Nam H. Jo under the direction of Editor Duk-Sun Shim.

Maryam Kazerooni received the M.Sc. degree from Shiraz University, Iran, in 2010. Since 2010, she is a Ph.D. candidate in Shiraz University of Iran. Her research interests include fault diagnosis and fault tolerant control for linear and nonlinear systems.

Alireza Khayatian received his Ph.D. degree in the Control Engineering from Georgia Institute of Technology 1993. He has been a faculty member with department of electrical engineering, since 1993. His research interests include Nonlinear Control, Estimation and Navigation.

Ali Akbar Safavi received his Ph.D. in Process Systems Engineering from Sydney University in 1995. His research interests are model predictive control, wavelets, neural networks, system identification, networked based Control, and information technology.

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Kazerooni, M., Khayatian, A. & Safavi, A.A. Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems. Int. J. Control Autom. Syst. 14, 569–578 (2016).

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  • Fault estimation
  • interconnected nonlinear systems
  • Lyapunov-Krasovskii approach
  • time delay