Existence of SDRE stabilizing feedback

J. S. Shamma, J. R. Cloutier

Research output: Contribution to journalConference articlepeer-review

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 paper, we consider the non-uniqueness of such a representation. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-shaped level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the roof is a novel application of the S-procedure for quadratic forms.

Original languageEnglish (US)
Pages (from-to)4253-4257
Number of pages5
JournalProceedings of the American Control Conference
Volume6
DOIs
StatePublished - 2001
Externally publishedYes
Event2001 American Control Conference - Arlington, VA, United States
Duration: Jun 25 2001Jun 27 2001

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Fingerprint

Dive into the research topics of 'Existence of SDRE stabilizing feedback'. Together they form a unique fingerprint.

Cite this