Analysis of second-order sliding-mode algorithms in the frequency domain

I. Boiko, L. Fridman, M. I. Castellanos

Research output: Contribution to journalArticlepeer-review

147 Scopus citations


A frequency domain analysis of the second-order sliding-mode algorithms, particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and Tsypkin's approach. It is shown that in the presence of an actuator, the transient process may converge to a periodic motion. Parameters of this periodic motion are analyzed. A comparison of the periodic solutions in the systems with higher order sliding-mode controllers and the oscillations that occur in classical sliding-mode systems with actuators is done.

Original languageBritish English
Pages (from-to)946-950
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 2004


  • Chattering
  • Relay control
  • Sliding-mode (SM)
  • Variable structure systems


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