# .Modelica_LinearSystems2.DiscreteStateSpace.timeResponse

## Information

#### Syntax

```    (y) = DiscreteStateSpace.timeResponse(dss, u)
or
(y, xc) = DiscreteStateSpace.timeResponse(dss, u, x0)
```

#### Description

This function calculates the time responses to input u of a discrete state space system. Default of initial state x0 is x0=0.

#### Example

```  import dss=Modelica_LinearSystems2.DiscreteStateSpace;
import Modelica_LinearSystems2.StateSpace;
StateSpace ss=Modelica_LinearSystems2.StateSpace(
A=[-1],
B=[1],
C=[2],
D=[0]);
Real Ts=0.1;
dss=dss(ss,Ts);
Real x0[1]={0};

Real y[:,:]=dss.timeResponse(dss,ones(51,1));

//  y=[0.09524, 0.2766, 0.4408,..., 1.9844, 1.9859, 1.9872]
```

#### Interface

```encapsulated function timeResponse
import Modelica;
import Modelica_LinearSystems2;
import Modelica_LinearSystems2.DiscreteStateSpace;
input DiscreteStateSpace sd "Linear system in discrete state space form";
input Real u[:, size(sd.B, 2)] = ones(3, size(sd.B, 2)) "System input (dimension: (input samples) x (number of inputs))";
input Real x0[size(sd.A, 1)] = zeros(size(sd.A, 1)) "Initial system state";
output Real y[size(u, 1), size(sd.C, 1)] "System response (dimension: (input samples) x (number of outputs))";
output Real x_continuous[size(u, 1), size(sd.A, 1)] "State trajectories (dimension: (input samples) x (number of states)";
end timeResponse;
```

## Revisions

Date Author Comment
2010-05-31 Marcus Baur, DLR-RM Realization

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