Markov Parameters

The *impulse response* of a state-space model is easily found by direct
calculation using Eq. (E.1):

Note that we have assumed
(*zero initial state* or
*zero initial conditions*). The notation
denotes a
matrix having along the diagonal and zeros
elsewhere.^{E.2}

The impulse response of the state-space model can be summarized as

(E.2) |

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.^{E.3} Therefore, it is not
a possible output signal, except when . A better name might be
``impulse-matrix response''. In
§E.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:

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