Abstract
In this paper, a well-posedness (existence and uniqueness of solutions) problem of bimodal systems given by two linear systems is addressed, where the definition of solutions of Carathéodory is used. This problem is a basic problem in the study of well-posedness for discontinuous dynamical systems. We give here a complete answer to this problem. The obtained result shows that the well-posedness of bimodal systems can be characterized by two properties: the preservation property of the lexicographic inequality relation between the two regions specifying the two modes, and the smooth continuation property.
This research has been performed while the first author being a research fellow of Canon foundation at Faculty of Mathematicak Sciences in University of Twente.
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Imura, Ji., van der Schaft, A. (1999). Well-Posedness of a Class of Piecewise Linear Systems with No Jumps. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_14
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DOI: https://doi.org/10.1007/3-540-48983-5_14
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