Kyiv Taras Shevchenko National University,
64 Volodymyrska Str.,
01017 Kyiv,
E-mail: cva@skif.kiev.ua

Matrix impulsive differential equations with impulses at variable times

The main purpose of the report is consideration of  the properties of solutions of impulsive matrix equations with impulses occurring at the moment of time when the phase point intersects given hypersurfaces in the extended phase space. These equations are more complicated than the equations with impulses at fixed times, which have been considered in our previous report [1]. In what follows, we will be considering impulsive equations the solutions of which intersect each hypersurface only once. Essential difference between equation with impulses at variable times and equation with fixed times of an impulsive effect is that solutions of first equation, in general, do not depend  on initial conditions continuously in such a way that this continuity be uniform on a finite interval. In our investigation the stability of solution of matrix impulsive equations with impulses at variable times have been proved.  Direct Lyapunov method for studying of stability of solutions of impulsive equations with impulses at variable times have been observed. Chesary's method for finding solutions of these equations have been considered. The questions of existence of a periodic solutions for these equations have been studied. The approximation of these solutions have been constructed.

  1. Chiricalov V.A. Matrix impulsive system of differential equations with bilinear main part, Proc. of Inst. of Mathematics of NAS of Ukraine, 2004, V.50, part 3, pp.1282-1287.