## Contents

## DINIT

Estimates the initial state, given estimated discrete-time state-space system matrices and a batch of measured input-output data.

## Syntax

`x0 = dinit(A,B,C,D,u,y)`

## Description

This function estimates the initial state for a measured input-output batch of a discrete-time LTI state-space model. The estimate is based on the measured input-output data sequences, and on the *A*, *B*, *C* and *D* matrices, which are possibly estimated using any of the subspace identification functions.

## Inputs

`A,B,C,D` is the discrete-time LTI state-space model.

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

## Outputs

`x0` is the estimated initial state.

## Algorithm

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

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

in which *yhatk)* is simulated using the estimated system matrices and the measured input *u(k)*. The function `ltiitr` is used to efficiently calculate *yhat(k)*.

## Used By

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

## Uses Functions

## See Also

## References

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