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

Héctor Ríos, 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 an 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, which do 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 the Lyapunov and input-to-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

Original languageEnglish
Pages (from-to)408-415
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - 1 Jan 2023

Bibliographical note

Funding Information:
Work in the authors' laboratories is funded by the Wellcome Trust, the Medical Research Council, and the Scientific Directorate of the Commission of the European Communities. We also thank DAVID DENHAM for permission to reproduce his data for Figure 1.

Publisher Copyright:
© 1963-2012 IEEE.


  • Adaptive observers
  • nonlinear systems
  • sliding-modes


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