ON FINDING STABILITY DOMAINS OF SYSTEMS OF DIFFERENTIAL-EQUATIONS WITH SMALL PARAMETERS AT THE DERIVATIVE

In automatic control theory, the following problem often arises [see V . I. Zubov, Mathematical Methods of Automatic Control Systems, Sudproi zdat, Leningrad (1959)]: ''The constant part of an automatic control s ystem is given, and there exist several free parameters determining th e functioning of control agents. We have to choose these parameters su ch that the fixed regime (stationary motion) is stable.'' In this pape r, we study this problem in the case of systems of differential equati ons with a small parameter at the derivative.