Adaptive backstepping control for a class of time delay systems with nonlinear perturbations

Chang Chun Hua, Qing Guo Wang, Xin Ping Guan

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


The sliding mode control method has been extensively employed to stabilize time delay systems with nonlinear perturbations. Although the resulting closed-loop systems have good transient and steady-state performances, the designed controllers are dependent on the time delays. But one knows that it is difficult to obtain the precise delay time in practical systems, especially when it is time varying. In this paper, we revisit the problem and use the backstepping method to construct the state feedback controller. First, a coordinate transformation is used to obtain a cascade time delay system. Then, a linear virtual control law is designed for the first subsystem. The memoryless controller is further constructed based on adaptive method for the second subsystem with the uncertainties bounded by linear function. By choosing new Lyapunov-Krasovskii functional, we show that the system state converges to zero asymptotically. Via the proposed approach, we also discuss the case that the uncertainties are bounded by nonlinear functions. Finally, simulations are done to verify the effectiveness of the main results obtained.

Original languageEnglish
Pages (from-to)289-305
Number of pages17
JournalInternational Journal of Adaptive Control and Signal Processing
Issue number3
Publication statusPublished - Apr 2008
Externally publishedYes


  • Backstepping method
  • Lyapunov-Krasovskii functional
  • Sliding mode control method
  • Time delay systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Electrical and Electronic Engineering


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