Main Content

State coordinate transformation for state-space model

`ss2ss`

performs the similarity transformation *z* = *T**x* on the state vector *x* of a state-space model. For more
information, see Algorithms.

`ss2ss`

performs the similarity transformation $$\overline{x}=Tx$$ on the state vector *x* of a state-space model.

This table summarizes the transformations returned by `ss2ss`

for each
model form.

Input Model | Transformed Model |
---|---|

Explicit state-space models of the form: $$\begin{array}{l}\dot{x}=Ax+Bu\\ y=Cx+Du\end{array}$$ |
$$\begin{array}{l}\dot{\overline{x}}=TA{T}^{-1}\overline{x}+TBu\\ y=C{T}^{-1}\overline{x}+Du\end{array}$$ |

Descriptor (implicit) state-space models for the form: $$\begin{array}{c}E\dot{x}=Ax+Bu\\ y=Cx+Du\end{array}$$ |
$$\begin{array}{c}E{T}^{-1}\dot{\overline{x}}=A{T}^{-1}\overline{x}+Bu\\ y=C{T}^{-1}\overline{x}+Du\end{array}$$ |

Identified state-space ( $$\begin{array}{c}\frac{dx}{dt}=Ax+Bu+Ke\\ y=Cx+Du+e\end{array}$$ |
$$\begin{array}{l}\dot{\overline{x}}=TA{T}^{-}{}^{1}\overline{x}+TBu+TKe\\ y=C{T}^{-}{}^{1}\overline{x}+Du+e\end{array}$$ |