Documentation

# ss2ss

State coordinate transformation for state-space model

## Syntax

```sysT = ss2ss(sys,T) ```

## Description

Given a state-space model `sys` with equations

`$\begin{array}{l}\stackrel{˙}{x}=Ax+Bu\\ y=Cx+Du\end{array}$`

or the innovations form used by the identified state-space (IDSS) models:

`$\begin{array}{c}\frac{dx}{dt}=Ax+Bu+Ke\\ y=Cx+Du+e\end{array}$`

(or their discrete-time counterpart), `ss2ss` performs the similarity transformation $\overline{x}=Tx$ on the state vector x and produces the equivalent state-space model `sysT` with equations.

`$\begin{array}{l}\stackrel{˙}{\overline{x}}=TA{T}^{-1}\overline{x}+TBu\\ y=C{T}^{-1}\overline{x}+Du\end{array}$`

or, in the case of an IDSS model:

`$\begin{array}{l}\stackrel{˙}{\overline{x}}=TA{T}^{-}{}^{1}\overline{x}+TBu+TKe\\ y=C{T}^{-}{}^{1}\overline{x}+Du+e\end{array}$`

`sysT = ss2ss(sys,T) ` returns the transformed state-space model `sysT` given `sys` and the state coordinate transformation `T`. The model `sys` must be in state-space form and the matrix `T` must be invertible. `ss2ss` is applicable to both continuous- and discrete-time models.

## Examples

Perform a similarity transform to improve the conditioning of the A matrix.

```T = balance(sys.A) sysb = ss2ss(sys,inv(T)) ``` 