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A polynomial approach to discrete-time non-linear system controllability

This paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input single-output (SISO) discrete-time non-linear systems. The condition is presented in terms of common factors of a non-commutative polynomial expression. This extends the result on controllability of linear systems and the recent result on controllability of continuous-time non-linear systems to expose controllability of discrete-time non-linear systems in the input–output framework. The controllability condition yields a finite step computing procedure for examining controllability of discrete-time input–output non-linear systems.