Brief Positive polynomial matrices and improved LMI robustness conditions

Authors:
Didier Henrion;Denis Arzelier;Dimitri Peaucelle
Affiliations:
Laboratoire d'Analyse et d'Architecture des Systèmes, Centre National de la Recherche Scientifique, 7 Avenue du Colonel Roche, 31077 Toulouse, France and Institute of Information Theory and A ...;Laboratoire d'Analyse et d'Architecture des Systèmes, Centre National de la Recherche Scientifique, 7 Avenue du Colonel Roche, 31077 Toulouse, France;Laboratoire d'Analyse et d'Architecture des Systèmes, Centre National de la Recherche Scientifique, 7 Avenue du Colonel Roche, 31077 Toulouse, France
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

Recently, several new LMI conditions for stability of linear systems have been proposed, introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions and intractable non-convex robust stability conditions. In this paper, we show that these improved LMI conditions can be derived with the help of some basic results on positive polynomial matrices. The approach allows us to derive in a unifying way results in the state-space and polynomial frameworks. Applications to robust stability analysis and robust stabilization of systems with multi-linear parametric uncertainty are fully described.