抄録
The existence of a discrete time bilinear system which is dynamically equivalent to a discrete time nonlinear system with C∞ nonlinear functions in the state and with the control appearing linearly, is assured. A procedure to construct a canonical form of such a bilinear system is the extension of Lo's method to a discrete time system, and there the power series expansion related to C∞ functions plays a great role. When this power series is finite, we obtain the input/output difference equations of the above bilinear system and a realizable bilinear system. When the series is infinite it can be shown that the asymptotic stability of the considered bilinear system is a sufficient condition for convergence of this power series.
