Construction of minimal realizations based on the generalized Markov parameters

Based on a generalization of the Markov parameters, a generalized method for the construction of minimal realizations is presented. The method can give a family of minimal realizations, which may be useful, for example, in the problem of minimal partial realization. In contrast to the Markov parameters, special forms of the generalized Markov parameters may readily be obtained from experimental data. In particular, it is shown that the Laguerre expansion coefficients of a system provide a special form of the generalized Markov parameters of an associated system, and by using the proposed method, an exact minimal state variable model of the system can be restored from its Laguerre truncation