Abstract: The event-based planning and control system is represented in terms of a non-time motion reference variable as its parameter and the relevant theories, such as stability analysis, controllability and observability and so on, are needed thorough research. For a certain type of input affine nonlinear systems, the event-based control system’s controllability problems will be investigated by using the nonlinear feedback linearization theory, and then nonholonomic event-based control systems’ controllability and observability are also investigated by using the controllability distribution and observability co-distribution conceptions in the nonlinear derivative geometry theory. A two differential wheeled drive mobile robot is studied as an application to analyze the relative theories. Some simulations about time-based control and event-based control with time delay are also conducted, and the simulation results show that the event based control method could overcome the effects brought by the random time delay, so the event-based control method is better for a time delay system than the time-based control method.

Key words: Controllability and observability, Nonholonomic, Random time-delay, Stability, Tele-operation