Model reduction techniques for sampled-data systems

An “approximately” balanced realization of linear finite-dimensional sampled-data systems is proposed. The theoretical support of the “approximately” balancing algorithm is represented by a result on the asymptotic expansions with respect to the sampling step of the sampled controllability and observability graminas. Reduced order models obtained as singular perturbational approximations of “approximately” balanced realizations of sampled-data systems are shown to be acceptable solutions to the sampled-data system model reduction problem in the sense that, enjoying some asymptotic properties, they come “close” to the exact solutions as the sampling step decreases. An example illustrates the results.