A Note about the Linear Time-Optimal Control Problem

In non-autonomous time-optimal control problems the question of the sufficiency of the maximum principle is considered. We also briefly discuss the question of uniqueness of optimal control. New conditions are obtained that guarantee the sufficiency of the maximum principle in terms of convex analysis, properties of matrices in the linear system, the geometry of the control set and the nonempty interior of some set-valued integrals. Examples that demonstrate the unimprovability of the obtained results are considered