On model reduction of K-power bilinear systems

As a special type of bilinear systems, K-power bilinear systems have a special coupled structure that should be preserved in the process of model reduction. We investigate moment matching methods for K-power systems and extract structure-preserved reduced models from the perspective of bilinear systems and coupled systems. The optimal H2 reduction is also considered for K-power systems. We prove that there exist reduced models satisfying the optimality conditions and meanwhile preserving the coupled structure of the original models. Furthermore, such reduced models can be produced by an iterative algorithm, or alternatively by a subsystem-iteration algorithm with less computational effort and faster convergence rate. Simulation results show that the proposed iterative algorithms possess superior performance in contrast to moment matching methods.