Covariance equivalent realizations of discrete systems
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Covariance equivalent realization theory has been used recently in continuous systems for model reduction and controller reduction. In model reduction, this technique produces a reduced-order model that matches q plus 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 plus 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 plus 1 covariances, 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. A new projection method is described which 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. 22 refs.
