Balanced truncation is the most commonly used model order reduction scheme in control engineering. This is due to its favorable properties of automatic stability preservation and the existence of a computable error bound, enabling the adaption of the reduced model order to a specified tolerance. It aims at minimizing the worst case error of the frequency response over the full infinite frequenc...

A direct method is developed that reduces a polynomial system matrix describing a discrete linear repetitive process to a 2-D singular state-space form such that all the relevant properties, including the zero structure of the system matrix, are retained. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D singular form is zero coprime syste...

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...