# Welcome to System-theoretic Model Order Reduction’s documentation!¶

System-theoretic model reduction seeks to build reduced order models based on metrics associated with the input-output map.
The simplest case appears in *linear, time-invariant* model reduction.
One common example is a state-space system relating input \(\mathbf{u}(t)\) to output \(\mathbf{y}(t)\) via the dynamical system

..math:

```
\mathbf{x}'(t) &= \mathbf{A} \mathbf{x}(t) + \mathbf{B} \mathbf{u}(t) \\
\mathbf{y}(t) &= \mathbf{C} \mathbf{x}(t).
```

The goal of the goal of *model reduction* is to construct a reduced order model mimicing
this input-output map.