State feedback linearization of nonlinear control systems on homogeneous time scales. (February 2019) - Bartosiewicz, Zbigniew; Belikov, Juri; Kotta, Ülle; Wyrwas, Małgorzata
Abstract: 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.