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8.1 Time-Domain System Identification
The problem of system identification in the time domain amounts to identifying matrices A, B, C, and D of the state-space system given a set of measured time-domain data. Only the discrete-time state-space system is considered here. Thus, given a set of output responses, which correspond to a set of input signals, the problem is to identify the matrices  ,  ,  , and  that satisfy the discrete-time state-space system:
Available are an infinite number of models that can predict the identical responses for any particular input. The one with the smallest state-space dimensions, called the minimal state-space realization, is of interest.
Two methods are implemented here. The first method is based on the explicit construction of Markov parameters. The second is a direct method in the sense that the system matrices are computed directly from the input-output data. Both methods are numerically effective.
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