Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 2009 | Published
Journal Article Open

Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties

Abstract

Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties.

Additional Information

© 2009 IEEE. Manuscript received March 05, 2009; revised June 17, 2009. First published September 22, 2009; current version published October 07, 2009. This work was supported in part under a NASA Langley NRA NNH077ZEA001N entitled "Analytical Validation Tools for Safety Critical Systems" and by the Air Force Office of Scientific Research, USAF, under Grant FA9550-05-1-0266. Recommended by Associate Editor H. Ito. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the U.S. Government. INSPEC Accession Number: 10917874.

Attached Files

Published - Seiler2009p6225Ieee_T_Automat_Contr.pdf

Files

Seiler2009p6225Ieee_T_Automat_Contr.pdf
Files (377.6 kB)
Name Size Download all
md5:7d299311c0d8d5e1c8058af10231e0f5
377.6 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 19, 2023