## Contents

## CSS2TH

Converts a parameter vector into a continuous-time LTI state-space model.

## Syntax

`[A,C] = cth2ss(theta,params)`

`[A,B,C] = cth2ss(theta,params)`

`[A,B,C,D] = cth2ss(theta,params)`

`[A,B,C,D,x0] = cth2ss(theta,params)`

`[A,B,C,D,x0,K] = cth2ss(theta,params)`

## Description

his function converts a parameter vector that describes a continuous-time state space model into the state space matrices of that model.

## Inputs

`theta` is the parameter vector describing the system.

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

`T` is the transformation matrix between the input state space system and the state space system in the form described by `theta`.

## Outputs

`A,B,C,D` are system matrices describing the state space system. If `theta` does not contain parameters for `D`, this matrix will be returned as an empty matrix.

`x0` is the initial state. If `theta` does not contain parameters for `x0`, this vector will be returned as an empty matrix.

`K` is the Kalman gain. If `theta` does not contain parameters for `K`, this vector will be returned as an empty matrix.

## Remarks

This function is based on the SMI Toolbox 2.0 function `cth2ss`, copyright 1996 Johan Bruls. Support for the omission of `D`, `x0` and/or `K` has been added, as well as support for the full parametrization.

## Algorithm

The model parametrization for the output normal form and the tridiagonal parametrization is carried out according to [1]. The full model parametrization is a simple vectorization of the system matrices. In its most general form, the parameter vector is given by

## Used By

## See Also

## References

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