Discrete Multivariable System Approximations 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 moment 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 maybe 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.