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This paper presents a hardware architecture for an embedded real-time generalized predictive control (GPC) algorithm based on the state-of-the-art Customizable Advanced Processor (CAP9) technology from Atmel; targeting automotive active suspension systems. The GPC algorithm relies on the solution of an optimization problem at every sampling period. Profiling shows that matrix operations consume the largest portion of the computation requirements of the algorithm. The proposed embedded system utilizes a systolic-array based matrix co-processor in order to accelerate matrix operations. The proposed embedded system is designed to fit within the proposed platform while meeting tight real-time constraints imposed by the automotive active suspension systems.