On the least time control problem with interior output constraints

A variational problem arising in the study of least time controls is formulated in terms of norms of functionals on suitable Banach spaces. The existence of a solution is demonstrated by an appeal to the Hahn-Banach theorem, and the form of solution is developed from the equality conditions for Hölder´s inequality. The systems being controlled are linear, but not necessarily time invariant, and the results may accordingly find application in the control of batch processing systems.