EXTERNAL REACHABILITY (REACHABILITY WITH POLE ASSIGNMENT BY PD FEEDBACK) FOR IMPLICIT DESCRIPTIONS

Even for flat implicit linear systems (i.e. having more state componen ts than state equations), reachability is a well defined concept in te rms of the set of state trajectories: it characterizes the property th at from any initial state can start a smooth state trajectory which re aches any final state. What can happen, however, for this general clas s of systems, is that a system with no control input can be completely reachable. We introduce here the notion of ''external reachability'' which expresses the fact that trajectories can actually be controlled through the input (by proportional and derivative state feedback). Geo metric necessary and sufficient conditions are given for external reac hability. A new design method is proposed for pole assignment which us es this concept and relies upon right inversion techniques.