We consider the problem of construction of the domain of attraction for systems with aftereffect. The structure of solutions
of the Cauchy problem in the vector space of states of a system is clarified with examples. We describe a constructive method
for the estimation of the domain of attraction from the inside with the use of the Lyapunov functions. This method is used
for the estimation of the effect of delay in a control device in the process of solution of the problem of uniaxial orientation
of a spacecraft.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 671–678, May, 1998.
The present work was partially supported by the Center for Fundamental Research in Economics.