| Abstract: | The structure at infinity of an ordinary differential control system is a finite sequence of increasing integers ending with the differential output rank of the system, namely the number of outputs that can be given as arbitrary functions of time when the inputs are unknown. Its definition and construction, originally done for linear systems, has been extended to affine nonlinear systems and used in order to study dynamic decoupling or model matching. It essentially relies on a state representation. The purpose of this paper is to make a critical examination of this concept and to modify it in order to avoid the state representation. At the same time, we extend it to nonlinear partial differential control systems by exhibiting a link with formal integrability, a highly important concept in the formal theory of systems of partial differential equations that cannot be handled by means of a transfer matrix approach. Many explicit examples will illustrate the main results and the possibility to use computer algebra techniques will be pointed out. |
