The impulse response terms for are known as the Markov parameters of the state-space model.
Note that each sample of the impulse response is a matrix.G.3 Therefore, it is not a possible output signal, except when . A better name might be ``impulse-matrix response''. In §G.4 below, we'll see that is the inverse z transform of the matrix transfer-function of the system.
Given an arbitrary input signal (and zero intial conditions ), the output signal is given by the convolution of the input signal with the impulse response:
Response from Initial Conditions
Time Domain Filter Estimation