q-Markov Covariance Equivalent Realizations

Model reduction based on regional pole and covariance equivalent realizations

“…A great many approaches are available in the literature on the general topic of model reduction, including aggregation methods [1], balancing techniques [2], Hankel norm approximation methods [3], H 1 norm approximations [4], and q-Markov covariance equivalent realizations [6], [7], [14], [15], to name just a few. A major drawback of each of these methods (with the exception of the q-Markov covariance equivalent realizations) is that the reduced-order models are not guaranteed to match any of the second-order information (i.e., covariance values) of the original model outputs, which is an important criterion when output performance is an item of interest.…”

“…In [6], [7], [14], and [15] a projection method has been used to obtain reducedorder models that match the first q + 1 output covariances and the first q-Markov parameters of the original model. These reduced models are called q-Markov covariance equivalent realizations, or "q-Markov covariance equivalent realizations (COVER's)."…”

“…However, complex transformations to specific coordinates were required in the literature associated with q-Markov COVER's (see, for example, [14] and [15] It is well known that the transient properties of linear time-invariant systems are influenced directly by the location region of the dominant poles, and hence the regional pole assignment problem has received great attention in recent years [8]- [10]. Therefore, instead of the qMarkov parameters used in [6], [7], [14], and [15], we utilize the dominant pole region to represent the transient performance index. It is clear that the region in which the dominant poles are situated and the steady-state output covariance value are closely related, respectively, to the transient and steady-state performance of linear time-invariant stochastic systems.…”