State estimation of state-dependent delay systems based on discretized switching model

In this paper, we focus on a position control system. In the system, an object moves along a line and regulates its position according to the distance measured by the signal reflection. The signal emitted from the object at a speed is reflected by the obstacle and detected by the object. Then the traveling time of the signal strictly depends on the emission and detection position of the object. How to estimate the current position and the speed from the traveling time is the main issue of this paper. This system is formulated as a state-dependent delay system. We then first represent the system as a discrete-time linear parameter varying system. Based on the fuzzy control theory, we can design a gain-scheduled observer. From some simulation results, we show the effectiveness of the method.