Robust Stability of System with M Input and N Output in a Class of Catastrophe “Hyperbolic Umbilic”

Abstract

The robust stability of control systems where the controlled object has dynamics is highlighted in present. This paper proposes a new approach to designing control systems for objects with uncertain parameters in the form of three-parameter structurally stable mappings. This method allows the synthesis of highly effective control system, which has wide field of robust stability. For a dynamic system affected by parametric uncertainty, this paper focuses on robust stability analysis of system with Lyapunov functions. This paper presents some theoretical fundamental results assisting in analyzing of the behavior of control systems, depending on parameter uncertainty. The obtained results are robust stability type since the robust stability is guaranteed under certain deviations from the current state. We developed a new method for the study of robust stability MIMO linear automatic control systems with m - inputs and n - output by constructing a vector Lyapunov function. Using the approach to the construction of Lyapunov functions, we have asymptotically stable stationary state of the control object. In fact, the results to provide dynamic safety and performance of control systems. Finally, conditions for robust stability is presented permitting to understand the application of the proposed approach.