Stabilization of system with pure delay in linear part

I.V.Grytsay, D.Ya.Khusainov

Kyiv National Taras Shevchenko University

64, Vladimirskaya Str., Kyiv, 01033, Ukraine

B.Půža

Masaryk University

Janáčkovo nám. 2a, Brno, 602 00, Czech Republic

 

In this paper the system with pure delay in linear part is considered. The conditions for asymptotic stability of the system were obtained. It is considered a problem of stabilization of the system with pure delay using feedback control on phase coordinates with delay. To stabilize the system we choose some control parameters with the help of the special form of characteristic quasipolynomial of the obtained system with pure delay. The problem of stabilization of the system with pure delay was also solved by using the feedback control on phase coordinates with delay. These results it is possible to use for investigation of problems of the long-term forecasting in economy, of biological problems, of oscillations and control systems problems.

grytsay@mail.univ.kiev.uaљљљ љљљљdkh@unicyb.kiev.uaљљљљљ љљљљpuza@math.muni.cz