Abstract: “In this paper we propose the problem of design control systems with increased potential of robust stability in a class of two- parametric structurally stable mappings for objects with m input and n output signals.For research of the stability of steady states we using the ideas of the second method A.M. Lyapunov and define components of the gradient vector of the Lyapunov function. During the studying 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, built in the two-parameter class of structurally stable, which will be sustained indefinitely in a wide range of uncertain parameters of the control object. This work presents novelty theoretical fundamental results assisting in analyzing of the behavior of control systems, meaning of r”

Keywords: control system, robust stability, structurally stable mappings, stability of steady States, geometric interpretation, stationary condition.