On one minimax problem with linear constraints

The paper is concerned with minimization of a function of the maximum of the linear and fractional rational fluction on a convex multigon in a finite dimensional space to which many optimization problems are reduced that arise in computer aided control. Properties of this maximum function are established which help find the minimum of that function on a convex multigo. The technique is easily computerized with the aid of standard algorithms of linear algebraical operations. Some extensions of the problem are discussed.