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A model reduction scheme of k-power bilinear systems is proposed in this work. The canonical state space structure of A-power systems is used to simplify a balancing like model reductton scheme for bilinear systems. The derived model reduction algorithm reduces to computational steps similar in complexity to the balanced approximation of linear systems. Controllability and observability gramians turn out to have simple block diagonal structures and their properties are easily derived. The simulation of an 11th

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