Euler’s discretization and dynamic equivalence of nonlinear control systems

Euler’s discretization transforms a nonlinear continuous-time system into a discrete-time one. It is shown that if two continuous-time systems are dynamically feedback equivalent then their Euler’s discretizations are dynamically feedback equivalent. Dynamical equivalence is characterized by isomorphism of differential or difference algebras associated to the systems. These algebras form two categories. Euler’s discretization defines a covariant functor from the category of differential algebras to the category of difference algebras.