# ctrb

Controllability of state-space model.

## Syntax

* Co = ctrb(A, B)
* Co = ctrb(sys)

## Input argument

* sys - State-space model
* A - State matrix: Nx-by-Nx matrix
* B - Input-to-state matrix: Nx-by-Nu matrix

## Output argument

* Co - Controllability matrix.

## Description

Controllability in a dynamic system refers to the system's ability to be guided to any desired state within a finite timeframe through the application of suitable control signals.

This property is commonly known as reachability.

The function ctrb is employed to calculate a controllability matrix, either from state matrices or a state-space model.

The resulting matrix serves as a tool to assess and confirm the controllability of the system.

## Example

```matlab
A = [1 2; 0 3];
B = [1; 1];
C = eye(2);
D = zeros(2, 1);
sys = ss(A, B, C, D);
Co = ctrb(sys)
```

## See also

[ctrbf](ctrbf), [obsv](obsv).

## History

| Version | Description     |
| ------- | --------------- |
| 1.0.0   | initial version |

## Author

Allan CORNET
