## Contents

## FFUNLTI

Calculates the cost-function information for `foptlti`.

## Syntax

`[epsilon] = ffunlti(th,H,params,timing)`

`[epsilon,psi] = ffunlti(th,H,params,timing)`

`[epsilon,psi,U2] = ffunlti(th,H,params,timing)`

## Description

This function implements the cost-fuction for `foptlti` frequency domain optimization framework. It is not meant for standalone use.

## Inputs

`th` is the parameter vector describing the system.

`H` is the frequency response function of the system to be optimized: an array of size *l* x *m* x *N* in which *H(:,:,i)* contains the complex FRF at the *i* th complex frequency.

`w` are the complex frequencies at which the FRF is measured.

`params` is a structure that contains the dimension parameters of the system, such as the order, the number of inputs, whether `D`, `x0` or `K` is present in the model.

`timing` must be either `'cont'` or `'disc'`, indicating that the supplied model is continuous of discrete time. Note that this influences *only* the way in which the output normal parametrization is built. The user is responsible for supplying suitable frequency data.

## Outputs

`epsilon` is the output of the cost function, which is the square of the error between the output and the estimated output.

`psi` is the Jacobian of epsilon.

`U2` is the left null-space of Manifold matrix for the full parametrization [1].

## Algorithm

The formation of the error-vector is done bu calculating the FRF of the current model:

The error-vector

is build up such that its *i* th blockrow consists of

, in which the real and imaginary components have been interleaved.

The Jacobian is formed efficiently by calculating FRFs as well. The formation of the Manifold matrix is performed according to [1]. A QR-factorization is used to obtain its left null-space.

## Used By

## Uses Functions

## See Also

## References

[1] L.H. Lee and K. Poolla, "Identification of linear parameter varying systems using nonlinear programming", *Journal of Dynamic Systems*, Measurement and Control, col. 121, pp. 71-78, Mar 1999.