A projection approach for model reduction by matching output covariances and Markov parameters

This paper describes a projection technique for model reduction to simultaneously match a specified number of output covariance derivatives and Markov parameters. COVariance Equivalent Realizations which match q + 1 covariance derivatives are called "q-COVERs." In general q-COVERS are not unique. The additional freedom is used herein so that the q-COVER obtained also matches q Markov parameters. The projection technique uses a form of the observability indices of the full order system to determine a priori the order required of the reduced order model to match a specified number of output covariance derivatives and Markov parameters. The resulting realization is shown to be independent of the basis of the complete model. Stability conditions for the reduced order model are also described, and the relationships are established between stochastically equivalent realizations and the q-COVERs.