Exact Linearization and Discretization of Nonlinear Systems Satisfying a Lagrange Pde Condition

A sufficient condition for exact linearization of a nonlinear system via an exponential transformation is obtained as a Lagrange partial differential equation. When its solution can be found, the transformation is determined such that the nonlinear systemis exactly converted into a linear system with arbitrary dynamics. When the transformation is invertible, this technique can be applied to exact discretization. Several examples are given to demonstrate the linearization and discretization processes and associated conditions. Asimulation result is presented to show that, under proper conditions, the obtained discrete-time model gives values that are identical to the continuous-time original at discrete-time instants for any sampling intervals.