Existence of SDRE stabilizing feedback

Jeff S. Shamma*, James R. Cloutier

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed-loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this note, we consider the nonuniqueness of state-dependent representations. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-convex level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the proof is a novel application of the S-procedure for quadratic forms.

Original languageEnglish (US)
Pages (from-to)513-517
Number of pages5
JournalIEEE Transactions on Automatic Control
Volume48
Issue number3
DOIs
StatePublished - Mar 2003
Externally publishedYes

Keywords

  • Gain scheduling
  • Nonlinear stabilization
  • Riccati equation

ASJC Scopus subject areas

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

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