  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.
