Symbolic Computation for Nonlinear Systems Using Quotients over Skew Polynomial Ring

Nonlinear control systems are more difficult to handle than linear, since the associativity is not valid. Laplace transforms and transfer functions, which form a symbolic computation for linear systems, are, therefore, disabled. A modern development of nonlinear control systems is thus related mainly to the systematic use of differential algebraic methods. However, such methods allow us to introduce similar symbolic computation also for nonlinear systems. To provide a basis for such a symbolic computation the theory of non-commutative polynomials over the field of meromorphic functions is introduced. In that respect, differential operators, which act on one-forms, play a key role. They form the left skew polynomial ring. Quotients of such polynomials stand for transfer functions of nonlinear systems. In other words, presented paper tries to show that there is no reason to believe well known dogma saying that nonlinear systems have no transfer functions.