Abstract
The paper proposes an approach to the construction of Lyapunov functions, which based on the geometric interpretation of a theorem on asymptotic stability and method of construction control systems with increased potential for robust stability for objects with uncertain parameters in the form of three-parameter structurally stable maps of catastrophe theory. Vector components of antigradient of Lyapunov function are set by components of the velocity vector (the right part of the equation of state). Conditions of robust stability obtained in the form of a system of inequalities for uncertain parameters of objects and set the parameters of the controller. The obtained results allow to build high-performance control system via increased potential robust stability. This approach provides dynamic security and performance of the system for any changes to uncertain parameters of the control object.