Some Applications of the Qualitative Maximum Principle

In this paper firstly we explain why we can use the condition ¿H/¿u =0 when applying the Qualitative Maximum Principle to solve the controllability problems for linear system. Then we give two applications of this principle. One of which is to prove a controllability criterion for the time varying linear system. The other is to give a theorem about the determination of the controllable region of linear time invariant system where it is not completely controllable. Together with other applications it can be seen that the Qualitative Maximum Principle may serve as the theoritical foundation for the controllability problems.