On the basis optimal control problems new principles of constructing bounded stabilizing feedbacks for dynamical systems are proposed. It is shown that the methods under question may be applied to stabilize control systems which are uncontrollable according to Kalman. On extremality of sets systems. New extremality notion is introduced for sets systems. It defines sets joint disposition in space.
Extrernal systems arise when investigating various optimization problems.
Extremality conditions are stated in the form of the generalized Euler equation and appear to be necessary and sufficient. Antonevich A.B., Lebedev A.V. Symbols of functional pseudodifferential operators in the scale of the Sobolev spaces. The strong perfect graph conjecture of Berge for line graphs of linear 3-colored hypergraphs. Kovalev M.M., Zaporozhets A.A., Girlikh E. Characterization of some subclasses of Monge matrices. On this basis we present a classification of matrices by using submodularity and convexity of the corresponding functions.