Reducibility and reduction of discrete-time nonlinear control systems: comparison of two approaches

The problem of system reduction is studied for discrete-time nonlinear single-input single-output systems described by high-order input-output (i/o) difference equations, that is, given the i/o equation, can one find a minimal representation which is equivalent to the original system with the order being as small as possible. Comparison of two notions of reducibility is provided. The reducibility properties addressed are both generalizations of the well-known notion of transfer equivalence to the case of nonlinear control systems. Two roles of transfer equivalence are covered by these extensions. The first is that of identity of the outputs for any fixed control sequence under zero initial conditions. The second role is that of pole/zero cancellation that may occur in the transfer function of equivalent systems. The relationship between two reducibility criteria related to two equivalence notions is examined and the reducibility criterion which extends pole/zero cancellation property is shown to be stronger. Finally, the computational aspects of system reduction are discussed.