H2 model reduction for SISO systems

Abstract The problem of approximating the impulse response of a discrete time linear time invariant single-input single-output system by one of lower order in a least squares sense is considered. Using Lagrange multipliers, a set of nonlinear equations is derived, which can be interpreted as a 'nonlinear' generalized singular value decomposition, in which the elements of the weights are quadratic functions of the components of the singular vectors. The problem is analyzed both in the time domain and the z -domain. An algorithm is derived that is inspired by inverse iteration.

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