Nonlinear norm-observability notions and stability of switched systems

João P. Hespanha, Daniel Liberzon, David Angeli, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review


This paper proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for norm-observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.

Original languageEnglish (US)
Pages (from-to)154-168
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2005


  • LaSalle's stability theorem
  • Nonlinear system
  • Observability
  • Switched system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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