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This dissertation is devoted to two main subjects, i.e. parameter identification and model reduction, of the modelling of discrete systems. The key concept that plays an important role in the dissertation is system response matching. By matching the system output responses, the model obtained is good enough to represent the original system. Two attractive approaches are adopted to deal with the matching processes. One applies orthogonal transformation to do spectrum matching between the output sequences of the original and desired models. The other uses the method of optimization to achieve an optimal time response matching between the original and reduced models. Both approaches possess an attractive feature. That is they always reduce the problem to the solution of a set of simultaneous linear algebraic equations. Thus the computational effort for system modelling is reduced considerably.
The problem of parameter identification is studied through the use of orthogonal spectrum matching. The designated input data sequence and the measured output data sequence of the system are first expanded into series of orthogonal polynomials, respectively.
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