A projection approach to covariance equivalent realizations of discrete systems

Structural system identification: from reality to models

“…System realization theory has been developed within the framework of linear dynamic systems analysis and control (see [17], for example). Realizations of linear systems are models which accurately express the system dynamics inherent in the transfer functions relating the system inputs and outputs [18][19][20]. State space realizations are relevant to modal testing because the first-order form encompasses all linear system behavior, including damped structural dynamics.…”

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)."…”

“…Due to the preservation of q > 0 output covariances, the q-Markov COVER provides a reduced-order model for continuous-and discrete-time systems that has the same steady-state covariance values of each of the multiple outputs as the original model, and due to the preservation of q-Markov parameters the q-Markov COVER also has the capacity to provide good transient approximation. 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.…”

“…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.…”