## Contents

## DAC2B

Estimates the *B* matrix in discrete-time LTI state-space models from input-output measurements.

## Syntax

`B = dac2bd(A,C,u,y)`

`B = dac2b(A,C,u1,y1,...,up,yp)`

## Description

This function estimates the *B* matrix corresponding to a discrete-time LTI state-space model. The estimate is based on the measured input-output data sequences, and on the *A* and *C* matrices, which are possibly estimated using `dmodpo`, `dmodpi` or `dmodrs`. The *D* matrix is assumed to be zero. Several data batches can be concatenated.

## Inputs

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

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

`u,y` is the measured input-output data from the system to be identified.

Multiple data batches can be specified by appending additional `u,y` pairs to the parameter list.

## Outputs

`B` is the state-space model's *B* matrix.

## Algorithm

Estimating `B` and the initial state `x0` from input-output data and `A` and `C` is a linear regression [1]:

The regression matrix `Phi` and data matrix `theta` are given by:

The function `ltiitr` is used to efficiently fill the regression matrix `Phi`.

## Used By

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

## Uses Functions

## See Also

`dac2bd`, `dmodpo`, `dmodpi`, `dmodrs`, `ltiitr`

## References

[1] B. Haverkamp, *Subspace Method Identification, Theory and Practice.* PhD thesis, Delft University of Technology, Delft, The Netherlands, 2000.