# Model Simplification Tools¶

`control.``balred`(sys, orders, method='truncate')

Balanced reduced order model of sys of a given order. States are eliminated based on Hankel singular value.

Parameters: sys: StateSpace : Original system to reduce orders: integer or array of integer : Desired order of reduced order model (if a vector, returns a vector of systems) method: string : Method of removing states, either `'truncate'` or `'matchdc'`. rsys: StateSpace : A reduced order model ValueError : if method is not `'truncate'` if eigenvalues of sys.A are not all in left half plane (sys must be stable) ImportError : if slycot routine ab09ad is not found

Examples

```>>> rsys = balred(sys, order, method='truncate')
```
`control.``hsvd`(sys)

Calculate the Hankel singular values.

Parameters: sys : StateSpace A state space system H : Matrix A list of Hankel singular values

`gram`

Notes

The Hankel singular values are the singular values of the Hankel operator. In practice, we compute the square root of the eigenvalues of the matrix formed by taking the product of the observability and controllability gramians. There are other (more efficient) methods based on solving the Lyapunov equation in a particular way (more details soon).

Examples

```>>> H = hsvd(sys)
```
`control.``modred`(sys, ELIM, method='matchdc')

Model reduction of sys by eliminating the states in ELIM using a given method.

Parameters: sys: StateSpace : Original system to reduce ELIM: array : Vector of states to eliminate method: string : Method of removing states in ELIM: either `'truncate'` or `'matchdc'`. rsys: StateSpace : A reduced order model ValueError : if method is not either `'matchdc'` or `'truncate'` if eigenvalues of sys.A are not all in left half plane (sys must be stable)

Examples

```>>> rsys = modred(sys, ELIM, method='truncate')
```