LMI approach to linear positive system analysis and synthesis - Équipe Méthodes et Algorithmes en Commande Accéder directement au contenu
Article Dans Une Revue Systems and Control Letters Année : 2014

LMI approach to linear positive system analysis and synthesis

Résumé

This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the performance of continuous-time positive systems. In addition, we further derive a new LMI for the performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback controller synthesis for discrete-time positive systems affected by parametric uncertainties.

Domaines

Automatique

Dates et versions

hal-01760867 , version 1 (06-04-2018)

Identifiants

Citer

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier. LMI approach to linear positive system analysis and synthesis. Systems and Control Letters, 2014, 63, pp.50 - 56. ⟨10.1016/j.sysconle.2013.11.001⟩. ⟨hal-01760867⟩
92 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More