On Variable-Transformation for Exact Discretization of First-Order n-th-Degree Nonlinear Systems

T. Kittaka, N. Hori (Japan), and C.A. Rabbath (Canada)


Nonlinear systems, discretetime modelling, exact linearization.


The present paper examines properties of an exact linearization method for a first-order n-th-degree nonlinear system via a variable transformation. A condition on the inverse variable transformation for obtaining an analytical solution is also investigated. An application of the linearization technique to exact discretization is then presented, where the resulting discrete-time model gives exact state responses at discrete-time instants for any discrete-time interval. It is shown that, knowing the initial state of the original nonlinear system and the present state of the linearized system, the present state of the nonlinear system can be determined uniquely. Simulation results are presented to support the claims.

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