Norm-Controllability of Nonlinear Systems

Matthias A. Muller, Daniel Liberzon, Frank Allgower

Research output: Contribution to journalArticlepeer-review


In this paper, we introduce and study the notion of norm-controllability for nonlinear systems. This property captures the responsiveness of a system with respect to applied inputs, which is quantified via the norm of an output. As a main contribution, we obtain several Lyapunov-like sufficient conditions for norm-controllability, some of which are based on higher-order derivatives of a Lyapunov-like function. Various aspects of the proposed concept and the sufficient conditions are illustrated by several examples, including a chemical reactor application. Furthermore, for the special case of linear systems, we establish connections between norm-controllability and standard controllability.

Original languageEnglish (US)
Article number7017484
Pages (from-to)1825-1840
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 1 2015


  • Controllability
  • Input-to-state stability (ISS)
  • Lyapunov methods
  • Nonlinear systems

ASJC Scopus subject areas

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


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