This paper presents system modeling, modified space vector PWM implementation (MSVPWM), and control system design of a Z-source converter. For an electrical analysis of the fuel cell powered systems, the fuel cell system is modeled by an R-C circuit including its voltage-current polarization characteristics. A discrete-time state space equation is given to implement digital control and a space vector pulse-width modulation technique is modified to realize the shoot-through zero vectors that boost the dc-link voltage. Three discrete-time controllers and an asymptotic observer are designed.