A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

Hector Rios, Roberto Franco, Alejandra Ferreira de Loza, Denis Efimov

Research output: Contribution to journalArticlepeer-review


A high-order sliding-mode adaptive observer is proposed to solve the problem of adaptive estimation, i.e., the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, that does not need to satisfy a relative degree condition equal to one. This approach is based on a high-order sliding-mode observer and a nonlinear parameter identification algorithm. The practical, global and uniform asymptotic stability of the adaptive estimation error, despite the external disturbances, is guaranteed through the small-gain theorem. The convergence proofs are developed based on Lyapunov and input-to-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

Original languageEnglish
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2021

Bibliographical note

Publisher Copyright:


  • Adaptive Observers
  • Adaptive systems
  • Asymptotic stability
  • Convergence
  • Estimation error
  • Measurement uncertainty
  • Nonlinear Systems
  • Nonlinear systems
  • Observers
  • SlidingModes


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