A Note on Aoki's Conditions for Path Controllability of Continuous-Time Dynamic Economic Systems
讨论动态路径可控性的充要条件，指出Aoki(1975)的秩条件在脉冲控制不可行时只是必要条件而非充分条件，并说明连续时间框架下Tinbergen的计数规则对任何目标与工具空间都是路径可控性的必要条件。
In this note we discuss necessary and sufficient conditions for dynamic path controllability, and show that the rank condition in Aoki (1975) is necessary but not sufficient unless impulse controls are admissible. It is demonstrated that in the special case of state space targets Tinbergen's concept of static controllability is equivalent to the dynamic concept of path controllability. For general linear systems conditions for path controllability depend on the choice of the admissible target and instrument space. In contrast to discrete-time models Tinbergen's original counting rule is necessary for path controllability for any target and instrument space in the continuous-time framework.