Differential rings associated with control systems on regular time scales

The paper develops an algebraic formalism of differential one-forms, associated with nonlinear control systems, defined on non-homogeneous, but regular time scales. The formalism unifies the existing theories for continuous and discrete-time systems and accommodates also the nonuniformly sampled systems. A ring of meromorphic functions, corresponding to a control system, is introduced. It is equipped with two operators whose properties are studied. An inversive closure of this ring is constructed. Compared with the homogeneous case the main difficulties are non-commutativity of delta derivative and shift operators and the fact that additional time variable t appears in the ring, associated to control system.