LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties. (November 2015)

• Record Type: Journal Article
• Authors: Adelipour, S.; Abooee, A.; Haeri, M.
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 37:Number 10(2015)
• Page Start: 1207
• Page End: 1216
• Publication Date: 2015-11
• Subjects: Interval uncertainty -- linear matrix inequality -- LTI-fractional-order system -- polytopic uncertainty -- robust stability analysis -- robust stabilization problem; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331214559120
• Languages: English
• ISSNs: 0142-3312

Abstract

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional orderα is a known constant belonging to0 < α < 1 . Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and stabilization problems.