# DiscrStateSpace

This block implements a discrete-time linear state-space system when activated at a fixed rate. The system is defined by the A,B,C,D matrices and the initial state x0.

## Library

Dynamical

## Description

This block implements a discrete-time linear state-space system when activated at a fixed rate.

The system is defined by the A,B,C,D matrices and the initial state vector x0.

The system is xdot = Ax + bu and y = Cx + du where x (size n) is the vector of the state variables, u is the vector of inputs (size m) and y (size r) is the vector of outputs.

## Parameters

Name | Label | Description | Data Type | Valid Values |
---|---|---|---|---|

| A matrix | real nxn matrix where n is the number of states, default value: 1. | Matrix | |

| B matrix | real nxm matrix where n is the number of states and m is the number of inputs, default value: 1. B=[ ] if block has no input. | Matrix | |

| C matrix | real rxn matrix, default value: 1. r is the number of outputs and n is the number of states. | Matrix | |

| D matrix | real rxm matrix where r is the number of outputs and m is the number of inputs, default value: 1. | Matrix | |

| Initial state | vector of size n or scalar (expanded to a vector of size n). | Vector | |

| External activation | Number | 0 |

## Ports

Name | Type | Description | IO Type | Number |
---|---|---|---|---|

| explicit | output | 1 | |

| explicit | input | 1 | |

| activation | input | externalActivation |

## Advanced Properties

Name | Value | Description |
---|---|---|

| no | |

| no, except when D is not zero | |

| no | |

| no | |

| no | |

| yes |