## DMODPI

Estimates the A and C matrix in a discrete-time state-space model from time-domain data that was preprocessed by dordpi.

## Syntax

[A,C] = dmodpi(R,n) [A,C] = dmodpi(R,n,'stable')

## Description

This function estimates the A and C matrices corresponding to an n th order discrete-time LTI state-space model. The compressed data matrix R from the preprocessor function dordpi is used to this end.

## Inputs

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

n is the desired model order n.

stable estimates a stable A matrix, see[1].

## Outputs

A is the state-space model's A matrix.

C is the state-space model's C matrix.

## Algorithm

The data matrix obtained with dordpi contains the weighted left singular vectors of the R32 matrix. The first n of these vectors form an estimate Os of the system's extended observability matrix:

The estimates Ahat and Chat are obtained by linear regression:

## Used By

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

[1] J.M. Maciejowski, "Guaranteed Stability with Subspace Methods",
Submitted to Systems and Control Letters, 1994.