Calculus of nonlinear interconnections with applications

Reports progress in the analysis of interconnections of nonlinear systems, employing the chronological formalism. A fundamental observation is the close analogy between feeding outputs of one system back as inputs to another system and the process of Lazard elimination which is at the root of Hall-Viennot bases and chronological products. Possible applications of the algebraic description of interconnections of systems include static and dynamic output feedback, and formal inversions of systems which are of interest for tracking problems. Our description in terms of iterated integral functionals is most readily applicable in the case of nilpotent systems, especially strictly triangular homogeneous systems