Output-input stability and minimum-phase nonlinear systems

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review


This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the "input-to-state stability" (ISS) philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.

Original languageEnglish (US)
Pages (from-to)422-436
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 2002


  • Adaptive control
  • Asymptotic stabilization
  • Detectability
  • Input-to-state stability (ISS)
  • Minimum phase
  • Nonlinear system
  • Relative degree

ASJC Scopus subject areas

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


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