Inverse optimality in robust stabilization

R. A. Freeman*, P. V. Kokotovic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

350 Scopus citations


The concept of a robust control Lyapunov function (rclf) is introduced, and it is shown that the existence of an rclf for a control-affine system is equivalent to robust stabilizability via continuous state feedback. This extends Artstein's theorem on nonlinear stabilizability to systems with disturbances. It is then shown that every rclf satisfies the steady-state Hamilton-Jacobi-Isaacs (HJI) equation associated with a meaningful game and that every member of a class of pointwise min-norm control laws is optimal for such a game. These control laws have desirable properties of optimality and can be computed directly from the rclf without solving the HJI equation for the upper value function.

Original languageEnglish (US)
Pages (from-to)1365-1391
Number of pages27
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - Jul 1996


  • Control Lyapunov functions
  • Differential games
  • Input-to-state stability
  • Nonlinear systems
  • Robust stabilization

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'Inverse optimality in robust stabilization'. Together they form a unique fingerprint.

Cite this