State feedback H∞ performance of fractional order systems

In this paper, the problem of state feedback H
∞
control of fractional order systems ( FOS) is considered. Firstly, some new theorems on stability and H
∞
performance of the continuous time FOS with 1 <α< 2 are established in terms of linear matrix inequality (LMI). Next, a necessary and sufficient condition for output feedback stabilizability is proposed, and iterative LMI (ILMI) algorithms are given to solve the conditions. An extension to output feedback H
∞
control is provided. Finally, a numerical example is given to illustrate the effectiveness of conclusion.