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Trajectory tracking control of bimodal piecewise affine systems. (English) Zbl 1088.93015

Summary: This paper deals with a trajectory tracking problem for a class of bimodal piecewise affine systems, which is inherently difficult 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 the inherent difficulty in trajectory tracking control 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. Furthermore, the feasibility condition of tracking for SISO piecewise linear systems is simplified. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
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