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Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1-gain and L-gain characterization


  • Corentin Briat

    Corresponding author
    1. Swiss Federal Institute of Technology–Zürich (ETH-Z), Department of Biosystems Science and Engineering (D-BSSE), Basel, Switzerland
    • Correspondence to: Corentin Briat, Swiss Federal Institute of Technology–Zurich (ETHZ), Department of Biosystems Science and Engineering (D-BSSE), Mattenstrasse 26, 4058 Basel, Switzerland.


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    • The author was previously with the ACCESS Linnaeus Centre, KTH, Stockholm, Sweden.


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 L1-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.

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