On stability and stabilization of motion with respect to a part of the variables
The comparison method, in case of Ljapunov vector functions, is applied in the investigation of partial stability of the motion of a system described by ordinary differential equations with continuous right-hand sides. A technique is developed which enables to solve the partial stabilization problem under certain requirements regarding the nature of transition processes of the system. To illustrate the applicability of the obtained results six examples are considered and solved. Finally, one discusses a technique and a method, both derived from the main results, which enable to solve partially the problem of minimizing the demand on resources and, respectively, to solve a functional minimization problem and a game theoretic problem on a minimax-maximin of a functional, with the scope of satisfying certain requirements regarding the transition processes with respect to a part of the variables.
scientific article; zbMATH DE number 3858980
scientific article