Covariance equivalent realizations of discrete systems

Covariance equivalent realization theory has been used recently in continuous systems for model reduction [1-4] and controller reduction [2, 5]. In model reduction, this technique produces a reduced-order model that matches q+1 output covariances and q Markov parameters of the full-order model. In controller reduction, it produces a reduced controller that is "close" to matching q+1 input covariances and q Markov parameters of the full-order controller. For discrete systems, a method was devised to produce a reduced-order model that matches the q+1 covariances [6], but not any Markov parameters; this method requires a factorization to obtain the input matrix, and thus may not maintain the original dimension of the input vector. The purpose of this paper is to describe a new projection method that matches q covariances and q Markov parameters of the original system. Since this technique is a projection method, it maintains the correct dimension of the input vector, and is therefore suitable for controller reduction as well. The earlier method [6] is not suitable for controller reduction since it does not maintain the correct dimension of the input vector.