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Analysis of Sliding Mode Observers Using a Novel Time-Averaged Lyapunov Function

[+] Author Affiliations
Sagar Mehta, Krishna Vijayaraghavan

Simon Fraser University, Surrey, BC, Canada

Paper No. DETC2017-68131, pp. V006T10A018; 9 pages
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5820-2
  • Copyright © 2017 by ASME


Sliding mode observers are known to be robust to model uncertainties. However, sliding mode observers have not been well analyzed in the presence of Gaussian disturbances and no previous results exist for a pure sliding mode observer in the presence of sensor noise. A traditional quadratic Lyapunov function that is used to determine the stability of sliding mode observers, fails for noisy systems. Hence this paper introduces a novel Lyapunov candidate function termed the time averaged Lyapunov (TAL) function to analyze the stability of noisy systems. The TAL specifically examines the effect of the Gaussian noise on a sliding mode observer. Using this TAL function, the paper demonstrates that Gaussian sensor noise does not affect the stability or chatter of the observer. Further, the covariance of the noise only affects the convergence rate of the observer. Simulation results are reported to demonstrate the effectiveness of the proposed approach on a Linear system.

Copyright © 2017 by ASME



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