Stabilization of Discrete-Time Nonlinear Systems Using Piecewise Multi-Linear Control Based on Input-Output Feedback Linearization

This paper proposes a discrete-time piecewise multi-linear system and a piecewise multi-linear controller based on input-output feedback linearizations. The modeling is easy because the piecewise model is constructed with only vertex values of the rectangle regions that divided the state space. The piecewise model is a nonlinear approximation and fully parametric. It is not difficult to analyze the stability of each region in piecewise system. However it is difficult to analyze the stability of the whole piecewise system. In this paper an input-output feedback linearization is used to transform each piecewise model into a linear system known as the Brunovsky canonical form. Thus the whole piecewise system can be stabilized by a feedback linearized controller. In addition, the state coordinate transformation vectors of the feedback linearization are easy to computable as a higher composition of the system and the output maps. Examples are shown to confirm the feasibility of our proposals by computer simulation.