Continuity of the Optimum Period of Performance as a Function of the Initial State of a Linear Controlled Object

A study is performed of the continuity of the optimum period of performance as a function of the initial state for a linear controlled object. The author generalizes parts of Theorem 21 and the proposition of Theorem 22 from Foundations of Optimal Control Theory by E. B. Lee and L. Markus on the continuity of the optimum period of performance as a function of the initial state of a controlled object. The support functions from convex analysis are widely used. Compared to more general known results based on more abstract mathematical methods, the results are constructive. The stationary case is considered in the first part of this work, and the nonstationary case is considered in the second.