The author was previously with the ACCESS Linnaeus Centre, KTH, Stockholm, Sweden.
Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1-gain and L∞-gain characterization
Article first published online: 21 JUN 2012
Copyright © 2012 John Wiley & Sons, Ltd.
International Journal of Robust and Nonlinear Control
Volume 23, Issue 17, pages 1932–1954, 25 November 2013
How to Cite
Briat, C. (2013), Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1-gain and L∞-gain characterization. Int. J. Robust Nonlinear Control, 23: 1932–1954. doi: 10.1002/rnc.2859
- Issue published online: 23 OCT 2013
- Article first published online: 21 JUN 2012
- Manuscript Accepted: 1 JUN 2012
- Manuscript Revised: 16 APR 2012
- Manuscript Received: 3 FEB 2011
- positive linear systems;
- integral linear constraints;
- robust control;
- robust linear programming;
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.