BUILT-IN MATHEMATICA SYMBOL

# StateResponse

StateResponse[ssm, u, {t, tmin, tmax}]
gives the numeric state response of the StateSpaceModel ssm to input u for .

StateResponse[ssm, {u[0], u[1], ...}]
gives the response of the discrete-time state-space model ssm to the input sequence .

StateResponse[ssm, u, t]
gives the symbolic state response as a function of time t.

StateResponse[ssm, {u1, ..., um}, ...]
gives the state response for multiple inputs .

StateResponse[{ssm, {x10, x20, ..., xn0}}, ..., ...]
gives the response with initial states .

## DetailsDetails

• StateResponse solves the state differential or difference equations for the given input.
• The initial states are taken to be zero unless specified.
• For descriptor systems, the initial states need to be consistent.
• For delay systems, the initial states include history and can be given as for t≤0. »

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

The state response of a continuous-time system to a unit step input:

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The response of a discrete-time system with initial conditions :

 Out[1]=

The state-response of a system to a Dirac delta input:

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 Out[2]=

The step response of a time-delay system:

 Out[2]=