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Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L 1 ‐gain and L ∞ ‐gain characterization
Author(s) -
Briat Corentin
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2859
Subject(s) - robustness (evolution) , linear programming , stability (learning theory) , linear system , mathematics , control theory (sociology) , lyapunov function , robust control , automatic gain control , mathematical optimization , computer science , control (management) , nonlinear system , control system , mathematical analysis , engineering , artificial intelligence , amplifier , computer network , chemistry , bandwidth (computing) , biochemistry , quantum mechanics , machine learning , physics , electrical engineering , gene
SUMMARY Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L 1 ‐gain and L ∞ ‐gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright © 2012 John Wiley & Sons, Ltd.