stability region of fractional order system

Question

I have a question about ellipsoid stability region of fractional order system with input saturation. In an integer system with input saturation we have the ellipsoid De as $ D_e=\left\{x(t)\in {\mathbb{R}}^n, {x }^T(t){P}x(t)\le {\beta }^{-1}\right\}$. My question is that, can we show the ellipsoid stability region of fractional order system with input saturation as below? $D_e=\left\{x (t)\in {{\mathbb{R}}^{n}};^C_{0}\mathfrak{D}_{{t}}^{-\left( 1-q \right)}\left( {{x}^{T}}\left( t \right){P}x( t) \right)\le {{\beta }^{-1}} \right\}.$