Fractional Generalized KYP Lemma for Fractional Order System within Finite Frequency Range

The celebrated GKYP is widely used in integer-order control system. However, when it comes to the fractional order system, there exists no such tool to solve problems. This paper prove the FGKYP which can be used in the analysis of problems in fractional order system. The $H_infty$ and $L_infty$ of fractional order system are analysed based on the FGKYP.