Abstract
This paper describes a controller and observer parameter definition approach in one input-one output (closed-loop) control systems using Lyapunov gradient-velocity vector function. Construction of the vector function is based on the gradient nature of the control systems and the parity of the vector functions with the potential function from the theory of catastrophe. Investigation of the closed-loop control system’s stability and solution of the problem of controller (determining the coefficient of magnitude matrix) and observer (calculation of the matrix elements of the observing equipment) synthesis is based on the direct methods of Lyapunov. The approach allows to select parameters based on the requested characteristics of the system.