## Contents

## 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.

## See Also

`dordpo`, `dmodpo`, `dordpi`, `dordrs`, `dmodrs`

## References

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