Abstract: “In this paper, we present a method increasing the potential of robust stability of control systems of spacecraft with an approach to the construction of two-parameter system in the class of structurally stable maps. Research of robust stability is produced by using the method of Lyapunov functions, based on geometric interpretation of the second Lyapunov method and definition of system stability in the state space. For research of the stability of steady states of spacecraft control system we using the ideas of the second method A.M. Lyapunov and define components of the gradient vector of the Lyapunov function. During the research, we will represent Equations of state in deviations relative to the stationary states. The general problem of Lyapunov functions for investigation of the systems with improved capacity of robust stability is defined and a condition of stability is given. We propose a method for construct the control system of spacecraft, built in the two-parameter class of s”

Keywords: control system, robust stability, increased potential of robust stability, structurally stable mappings, geometric interpretation.