Trajectory tracking control of bimodal piecewise affine systems

This paper deals with a trajectory tracking problem of a class of bimodal piecewise affine systems, which have rarely been discussed so far. This would be very challenging because of the discontinuous changes of their vector fields. First, we introduce an error variable and an error system as a generalization of the tracking error and its system. As an error variable, a function switched by the mode of a piecewise affine system is adopted to overcome an inherent difficulty in trajectory tracking of piecewise affine systems. Next, we design a tracking controller which stabilizes the error system using a Lyapunov-like function, which can be applied to systems including state jumps. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.