On relative degree, chattering and fractal nature of parasitic dynamics in sliding mode control

With respect to relative degree and chattering in sliding mode (SM) control systems, the notion of fractal dynamics is introduced, and a conjecture is formulated that the character of parasitic dynamics of real control systems is fractal. A model of fractal dynamics is proposed. The characteristics of fractal dynamics are studied in the frequency and time domains. It is shown that with fractal parasitic dynamics SM control systems will always feature chattering and non-ideal closed-loop performance. An example of analysis is provided.