A least squares approach to reduce stable discrete linear systems preserving their stability. (Q1430377)

As it is known, the problem of model reduction for an \(n\)-dimensional stable discrete linear single-input-single-output \(S\), consists of the replacement of \(S\) by another system \(S'\) whose dimension \(m\) to be much smaller than \(n\) and so that the main properties of \(S\) are still guaranteed with the new system. In this respect, stability is one of the most usual properties to be preserved which can not be generally assured when using the classical Padé approximation method. In his paper, a model reduction based upon the so called ``balanced truncation method'' is analyzed. The main advantage of the proposed method is that the solution of the two corresponding \(n\)-dimensional Stein equations can be now efficiently performed.