Fuel cell is a power supply system, which takes advantage of the electro-chemical reaction between oxygen and hydrogen to produce electricity with water as its byproduct. Due to their lower pollution and high efficiency compared with fossil fuels, fuel cell systems are under extensive development for many power applications. Compared with high temperature fuel cells (such as molten carbonate fuel cells or solid oxide fuel cells), the proton exchange membrane fuel cell (PEMFC) is more suitable for automotive applications because of its low temperature working condition, thereby a fast startup.Air compressor supplying the oxygen to the stack is an important component in the fuel cell systems. The compressor can consumes up to 20 % of the generated power in the most severe cases. The selecting of the compressor and corresponding control are directly related to the performance of the fuel cell. The size and weight of the air compressor has to be reduced to make them more feasible for automotive applications. Moreover, the control of the air compression system is also an important issue, which affects the efficiency and the safety of the fuel cell. To avoid oxygen starvation of the stack, the mass flow of the supplied air has to be controlled appropriately according to the load demand. Meanwhile, the pressure should not have large deviations or ripples which may damage the stack membrane.In this thesis, the requirements to the compressor for fuel cell applications are discussed. And several kinds of compressor are compared, including positive displacement types and dynamic superchargers. In the view of compactness, an ultra-high speed, up to 280,000 rpm, centrifugal compressor is adopted. The centrifugal compressor which is a kind of dynamics superchargers converts the kinetic energy of the air to the pressure. Compared with positive displacement compressors, it has the advantages of compactness, high efficiency and low noise, making it more suitable for automotive applications. However, the difficulty of the control as well as the surge iv constraint obstructs its industrial implementation for fuel cells.In this dissertation, The model of the air compression system is developed and the coupling between the model inputs and outputs are analyzed. The compressor map is measured and then fitted by a two hidden layer neural network model. The relative gain array (RGA) method is used for the coupling analysis. It shows that the coupling degree varies as the operation point changes because of the nonlinearity of the system. The second part of this work focuses on solving the control problems to adapt the centrifugal compressor to the fuel cell system. The objective is to control the mass flow and pressure simultaneously according to the fuel cell load demand. The problem lies in the coupling between the mass flow control and pressure control because the variations of one variable will also lead to the deviation of the other one. The interaction between the two control loops declines the performance of the fuel cell...