Trajectory Tracking Control of Bimodal Piecewise Affine Systems

This paper deals with a trajectory tracking problem of a class of bimodal piecewise affine systems. First, we introduce an error variable as a generalization of the tracking error. A discontinuous function is adopted as an error variable to overcome an inherent difficulty in tracking of piecewise affine systems. Next, the system which governs the error variable is guaranteed to be locally stable using a Lyapunov-like function, which yields trajectory tracking of the original system. Furthermore, we propose a procedure to extend the local result to a global one. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.