Local realization of linear and nonlinear time-varying systems

The aim of this paper is to present an algebraic theory of the realization of linear and nonlinear time-varying systems. In the linear case, the correspondence between Kalman´s factorization criterion and the representative functions leads to a very simple and transparent formulation of the realization theory. In the nonlinear case, the time-varying realization is related to the strong controllability of the system. The connection between linear and nonlinear time-varying systems is investigated by using noncommutative generating series.