The Markov parameter sequence for a state-space model is a kind of matrix impulse response that easily found by direct calculation using Eq.(G.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.G.2 Since the system input is a
vector, we may
regard
as a sequence of
successive input vectors, each
providing an impulse at one of the input components.
The impulse response of the state-space model can be summarized as
![]() |
(G.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.G.3 Therefore,
it is not a possible output signal, except when
. A better name
might be ``impulse-matrix response''. It can be viewed as a sequence
of
outputs, each
. 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: