Abstract: “We propose an approach to design of robust stability of dynamic control systems with one input and one output signals. Design of robust stability of control system is based upon construction A.M. Lyapunov’s function. The system states the method of construction of A.M. Lyapunov’s function on the basis of geometric interpretation of Lyapunov theorems concerning asymptotic stability and concepts of dynamic systems stability. It is supposed that undisturbed motion of system corresponds to origin of coordinates, and equations of state are comprised as regard to perturbances, i.e. in deviations of perturbational motion. Hence, equations of state evaluate the rate of change of perturbance (disturbance) vector and in stable system is directed to origin of coordinates. Gradient vector from Lyapunov required function is directed to the side opposite. Construction of Lyapunov vector function and development of robust stability of dynamic control system with undetermined parameters is based on co”

Keywords: Control systems, robust stability, superstability, Lyapunov’s direct method, modelling, simulation.