On the positive invariance of polyhedral sets in fractional-order linear systems

Abstract

In this paper, we derive conditions for a given polyhedral set to be a positively invariant set with respect to fractional-order linear time-invariant (FO-LTI) systems with fractional order of 0 < alpha < 1. FO-LTI systems are described using Riemann-Liouville operator with initialization response. Then, the conditions are obtained from Farkas&apos; lemma and the definition of the Mittag-Leffler function. Furthermore, we apply these conditions to the constrained stabilization. (C) 2013 Elsevier Ltd. All rights reserved.