Indian Journal of Science and Technology

Abstract

Background/Objectives: In this paper proposes a new approach to the study robust stability of system in the class of 3-parameter structurally steady maps. Methods/Statistical Analysis: The research is based on a novelty approach derived from the geometric interpretation of Lyapunov theorem. Lyapunov functions is synthesized in the form of vector functions, and its antigradient sets in the specified component of the velocity vector of system in the form of velocity tensor. The region of system stationary states stability is obtained in the form of simple inequalities for uncertain parameters of the control object. Findings: The proposed aspect to choice control laws for linearized system in a class of three-parameter structurally stable maps from catastrophe theory allows to the construct an automatic control system with a marginal increased potential of robust stability. Synthesized control system maintains stability property in an extremely wide range of object uncertain parameters and given system parameters. Also, the results of experimental laboratory research in the Simulink Matlab show, that the proposed system have higher quality. Application/Improvements: An example showing the effectiveness of the method in aircraft control systems.
Keywords: Three-Parameter Structurally Stable Maps, Lyapunov’s Function, Robust Stability, Control Aircraft, Angular Motion