## Contents

## DORDRS

Preprocesses time-domain data for the iterative Reconstructed State RS-MOESP algorithm to identify discrete-time state-space models. Delivers an order-estimate.

## Syntax

`[S,R] = dordrs(u,y,x,s)`

`[S,R] = dordrs(u,y,x,s,Rold)`

## Description

This function performs the initial data compression for RS-MOESP subspace identification based on measured input-output data [1] and a reconstructed state from a previous model estimate [1]. In addition, it delivers information usuable for determining the required model order. The model structure is the following

Here, *v(k)* is zero-mean noise of arbitary color, independent of the noise-free input *u(k)* . Several data batches can be concatenated, as shown below. This function acts as a preprocessor to `dmodrs`.

## Inputs

`u,y` is the measured input and output data of the system to be identified.

`x` is the reconstructed state. This state can be obtained by simualting the state0equation belonging to the previous model estimate's *Ahat* and *Bhat* matrices:

This initial model can be obtained by e.g. PI-MOESP.

`s` is the block-size parameter. This scalar should be *>n*.

`Rold` is the (optional) data-matrix resulting from a previous call to `dordrs`.

## Outputs

`S` is the first *s* singular values of the rank-deficient *R32* matrix (see below).

`R` is a compressed data matrix containing information about the measured data, as well as information regarding the system dimensions.

## Algorithm

The discrete-time data compression algorithm in [1] is used. The following RQ-factorization is made:

The meaning of the various matrices can be found in the cited article. A weighted SVD of the *R32* matrix is made, and its left singular vectors are appended to the `R`-matrix. Its first *s* singular values are returned in `S`.

## Used By

This a top-level function that is used directly by the user.

## See Also

`dordpo`, `dmodpo`, `dordpi`, `dmodpi`, `dmodrs`

## References

[1] M. Verheagen, "Identification of the deterministic part of MIMO state space models given in innovations form from input-output data", *Automatica*, vol. 30, no. 1, pp. 61-74, 1994.