1 State-feedback control with a prescribed rate of exponential convergence

Ian J. Fialho, Tryphon T. Georgiou

Research output: Contribution to journalArticle

9 Scopus citations


In this paper we consider the ℓ1 -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ1 performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ1-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ1 performance.

Original languageEnglish (US)
Pages (from-to)1476-1481
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Dec 1 1997


  • Controlled-invariant sets
  • Isaacs equation
  • ℓ control

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