This paper investigates semi-active vibration control using Fluidic Flexible Matrix Composites (F2MC) as variable stiffness components of flexible structures. The stiffness of F2MC tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the F2MC tube changes the internal volume when externally loaded. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. When the valve is closed, the high bulk modulus fluid resists volume change and produces high stiffness. The equations of motion of an F2MC-mass system is derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. To capture the important system parameters, nondimensional full order and reduced order models are developed. A Zero Vibration (ZV) state switch technique is introduced that suppresses vibration in finite time, and is compared to conventional Skyhook semi- active control. The ITAE performance of the controllers is optimized by adjusting the open valve flow coefficient. Simulation results show that the optimal ZV controller outperforms the optimal Skyhook controller by 13% and 60% for impulse and step response, respectively.