EVALUATION TRANSFORM AND SYMBOLIC-CALCULUS FOR NONLINEAR CONTROL-SYSTEMS

Given a nonlinear control system, one can view its output function as a signal, parametrized by the primitives of the input functions. This signal can be formally described by its Fliess' power series, that is a formal power series on noncommuting variables. The temporal behaviour of the system can be derived from this symbolic description by a transform, that we call ''Evaluation transform'' and that generalizes the inverse Laplace transform to the nonlinear area. We developpe here the basic tools of that symbolic calculus by introducing a ''kernel'' for our Evaluation transform. This kernel can be viewed as some ''temporal memory'' of the system in the Volterra's meaning as well as in the programmation meaning.