Abstract
The current article introduces a new method of construction of control systems for objects with uncertain parameters in the form of three-parameter structurally stable mappings from the theory of catastrophe, allowing to synthesize the highly effective control systems, which demonstrate the extremely wide range of robust stability. The research of robust stability of control systems is based on a new approach to post-rhenium of the A.M Lyapunov’s functions. The method of creation of control system with the increased potential of robust stability is stated. It could be concluded that the application of the suggested approach may assure asymptotically stable invariant states for the system in both negative and positive regions of variations of uncertain parameters.