International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This article is about robust stable control system for objects with uncertain parameters with an approach to the choice of control laws in the class of four parametric structurally stable mappings, which allow increasing the robust stability potential and the quality of the control system. This article presents robust stability of a system with one input and one output in the class of catastrophe functions "parabolic umbilic". To study the robust stability of stationary states of the system, the main provisions of the Lyapunov function method are used.

The article considers approach to construction of control system with increased potential of robust stability of spacecraft in the class of three-parametric structurally stable mappings. Since modern control systems are developed and operated in conditions of significant uncertainty, increasing the potential of system’s robust stability is one of the key factors that guarantee the system of protection against the generation of deterministic chaos and instability. In this regard, in conditions of great uncertainty, to build a control system with rather wide area of robust stability is proposed a method for constructing Lyapunov functions based on the geometric interpretation of Lyapunov’s theorems on asymptotic stability and dynamic systems stability concepts.