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This paper investigates a meaning of reference tracking control with respect to relative degree. Not only time functions but also functions of state variables are chosen as a reference. The problem setting using a reference with state variable is sometimes, referred to as a synchronization problem. In this paper, the example of failure of reference tracking control using state reference function is introduced, and what happened in this example is analyzed. Finally, the necessary condition for achieving the reference tracking control is stated.

This paper addresses controller switching problem based on input-output linearization. In input-output linearization, controller switching is achieved by switching the time invariant linearizing outputs. The feature of this paper is to focus on keeping output zero via time-varying output to utilize an advantage of input-output linearization. Time-varying process must be designed to connect two zero submanifolds with respect to time-invariant outputs smoothly so that once output zeroing is achieved, output zero is maintained during time-varying process. This paper provides the condition of time-varying output functions to keep output zero.