The analysis of control systems with a high potential for robust stability on the control object output

Abstract

This paper considers control systems with an increased potential for robust stability in the output
of an object in the class of one-parameter structurally stable mappings from catastrophe theory.
The actual problem is the design of control systems that provide in some sense the best protection
against uncertainty in the knowledge of the properties of an object and the instability of control
systems. The ability of a control system to maintain stability under parametric or non-parametric
uncertainty is understood as the robustness of the system. In the general formulation of the
study of the system for robust stability, it is necessary to indicate the restrictions applied to the
fluctuation of uncertain parameters of the control system, under which stability is maintained. A
large number of papers have been devoted to the problem of studying robust stability of control
systems. The study of the dynamic compensator with a high potential for robust stability is
performed by the gradient-velocity method of Lyapunov vector functions. The area of robust
stability of the control system for the object output is obtained in the form of a system of the
simplest inequalities for the matrix of controller parameters and the monitoring device. The
proposed gradient-velocity method of Lyapunov vector functions in the study of the output
control system of the object eliminates complex and ambiguous calculations and canonical
transformations and allows one to determine the region of choice of controller parameters and the
observer, providing the desired transition characteristics of a closed system.