Nonlinear state feedback for ℓ1 optimal control

Jeff S. Shamma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


This paper considers ℓ1 optimal control problems with full state feedback. In contrast to H optimal control, previous work has shown that linear ℓ1 optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.

Original languageEnglish (US)
Pages (from-to)265-270
Number of pages6
JournalSystems and Control Letters
Issue number4
StatePublished - Oct 1993
Externally publishedYes


  • Disturbance rejection
  • nonlinear compensation
  • state feedback
  • viability theory
  • ℓ optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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