Well-Posedness of a Class of Piecewise Affine Systems
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The well-posedness problem (existence and uniqueness of solutions) of a class of piecewise affine (PWA) systems is addressed. First, two kinds of discrete transition rules, i.e., the mode-based rule and the switch-based rule, are introduced to define the concept of solutions of PWA systems. Next, after several fundamental tools for the well-posedness analysis are given, necessary and/or sufficient conditions for the system to be well-posed are presented.
KeywordsHybrid systems Piecewise affine systems Well-posedness Transition rule Switches
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