Partial Realization in Generalized Bases: Algorithm and Example

A solution is presented for the problem of realizing a minimal state-space model of an LTI discrete-time system from a partial expansion in terms of generalized orthonormal basis functions, also known as Hambo basis functions. For the solution of the minimal partial realization problem fruitful use is made of the Hambo operator transform theory that underlies the basis function expansion. The resulting realization algorithm can be applied in an approximative sense, for instance for the computation of a low order model from a large basis function expansion that is obtained in an identification experiment. This approach is illustrated with an example.