A PROJECTION APPROACH TO COVARIANCE EQUIVALENT REALIZATIONS OF DISCRETE-SYSTEMS

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 output covariances of the full-order controller, and q Markov parameters of the closed-loop system. 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 since the dimension of this matrix factor depends on rank properties not known a priori, this method may not maintain the original dimension of the input vector. Hence, this method is obviously not suitable for controller reduction. A projection method is described that matches q covariances and q Markov parameters of the original system while maintaining the correct dimension of the input vector.