Abstarct: In this thesis, a new technique has been considered to design of the stabilizer control baxsed on Jacobi pseudo-spectral method.At first, we study the conditions of the stability of integer and fractional systems, then we use the theorems and definitions related to Lyapunov stability. finally, we present a new theorem and prove theorem, stability of infinite horizon control system. For this purpose, first we transform the system to a finite horizon fractional control system and then we to a algebraic system with approximation variables state and control and using Jacobi-Gauss nodes.