Robust H ∞ analysis and control of fractional-order systems with convex polytopic uncertainties

In this paper, the problem of robust H ∞ analysis and control of fractional-order linear time-invariant systems subjected to polytopic uncertainties are investigated. A sufficient condition for the H ∞ performance analysis of fractional-order polytopic systems is established in terms of linear matrix inequalities via the H ∞ bounded real lemma for commensurate fractional-order systems. Based on this condition, a LMI method for the design of robust H ∞ controller is obtained. Next, a less conservative condition for the H ∞ performance analysis of such systems is introduced. Finally, two different numerical examples are provided to demonstrate the effectiveness of the proposed approaches.