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Mathematics of Control, Signals and Systems

, Volume 18, Issue 1, pp 32–65 | Cite as

Global complete observability and output-to-state stability imply the existence of a globally convergent observer

  • Alessandro Astolfi
  • Laurent Praly
Article

Abstract

We consider systems which are globally completely observable and output-to-state stable. The former property guarantees the existence of coordinates such that the dynamics can be expressed in observability form. The latter property guarantees the existence of a state norm observer and therefore the possibility of bounding any continuous state functions. Both properties allow to conceptually build an observer from an approximation of an exponentially attractive invariant manifold in the space of the system state and an output driven dynamic extension. The proposed observer provides convergence to zero of the estimation error within the domain of definition of the solutions.

Keywords

Non linear observers Output-to-state stability Invariant manifolds 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentImperial College LondonLondonUK
  2. 2.Dipartimento di Informatica, Sistemi e ProduzioneUniversità di Roma Tor VergataRomaItaly
  3. 3.Centre Automatique et SystèmesÉcole des Mines de ParisFontainebleauFrance

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