Energetic parameters in approximation of discrete systems: a MIMO extension problem

An extension of the use of three model reduction techniques to the MIMO linear discrete time systems is presented, in this paper. The main idea is the use of some intrinsic ingredient of the complete order original system namely the impulse response gramian of the complete order system and the Hankel singular values in the construction of various approximants. These models have been compared to the same order reduced model given by the internal projections method. To see the efficiency of each algorithm, these methods are implemented and several simulations are done. From an illustrative example and by means of two important norms, we can better appreciate the most efficient one.