Discrete multivariable systems approximation by minimal pade type stable models

The approximation of discrete-time multivariable high order linear systems is considered. Reduced order models are derived by a generalized minimal partial realization algorithm. The derived models approximate the system in the Pade-sense and the presented method overcomes some serious limitations of former multivariable reduction methods. The set of all different models of minimal order that approximate a mixed sequence of Markov and time matrices of a given length is characterized by the common structural properties of these models. A maximal set of free parameters for the above set of all models is determined. These parameters can assign values independently and can be used to satisfy further desired specifications. A procedure is presented to solve the problem of possible instability of Pade approximated models of a stable system. Stable models may be chosen among the models of the same minimal order that differently emphasize the approximation of the steady-state and the transient responses. When applicable, the free parameters can also be adjusted to yield stable models. Finally, a complementary systematic method is presented by which unstable models can be replaced by a stable model of the same order and with the same singular values that approximate, in the Pade sense, the magnitude of the high order system.