## Markov Parameters

The impulse response of a state-space model is 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

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''. 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:

 (G.3)

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