State feedback linearization of nonlinear control systems on homogeneous time scales

The paper addresses the state feedback linearization problem for nonlinear systems, defined on homogeneous time scale. Necessary and sufficient solvability conditions are given within the algebraic framework of differential one-forms. The conditions concerning the exact dynamic state feedback linearization are equivalent to the property of differential flatness of the system. An output function which defines a right invertible system without zero-dynamics is shown to exist if and only if the basis of some space of one-forms can be transformed, via polynomial matrix operator over the field of meromorphic functions, into a system of exact one-forms. The results extend the corresponding results for the continuous-time case.