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

The initial conditions are assumed to be zero:

Specify

as the initial state values:

The state response of a three-input system to inputs

{Sin[t], Cos[t], Cos[t]}:

Plot the response:

If the number of input signals is less than the number of the system's inputs, the remaining inputs are assumed to be zero:

If a scalar input signal is specified for a multiple-input system, the signal is applied to each input channel in turn:

StateResponse gives the result in terms of interpolating function objects:

Plot the response:

The state response for a generic continuous-time system:

The response to a unit step input:

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

The state response to a sampled sinusoid:

Plot the response with a zero-order hold:

The state response of a two-input system to two randomly sampled inputs:

If the number of sampled inputs is less than the number of system inputs, the remaining inputs are assumed to be zero:

The second and fourth states are not excited because the second input is zero:

If only a single-input sequence is given to a multi-input system, the sequence is applied to each input in turn:

For this system, the first input excites only the first and fourth states, the second input excites only the second and fifth states, and the third input excites only the third and sixth states:

The response for a generic discrete-time system:

The response to a unit step sequence: