@article{8403f355a88e4e54a7d70ba67c607775,
title = "Common Lyapunov functions and gradient algorithms",
abstract = "This note is concerned with the problem of finding a quadratic common Lyapunov function for a large family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.",
keywords = "Common Lyapunov functions, Gradient algorithms, Randomized algorithms, Switched linear systems",
author = "Daniel Liberzon and Roberto Tempo",
note = "Funding Information: Manuscript received September 10, 2002; revised April 14, 2003 and January 20, 2004. Recommended by Associate Editor A. Bemporad. The work of D. Liberzon was supported by the National Science Foundation under Grant ECS-0134115 CAR, ECS-0114725 and by DARPA/AFOSR und er Grant MURI F49620-02-1-0325. Funding Information: The authors would like to thank B. R. Barmish, G. Dullerud , Y. Fu-jisaki, C. Hadjicostis, and B. Polyak for helpful discussions. This research was performed in part while R. Tempo was visiting the Coord i-nated Science Laboratory at the University of Illinois as a CSL Visiting Research Professor; the support of this program is gratefully acknowledged.",
year = "2004",
month = jun,
doi = "10.1109/TAC.2004.829632",
language = "English (US)",
volume = "49",
pages = "990--994",
journal = "IRE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",
}