Well-posedness analysis of switch-driven hybrid systems

A class of multimodal hybrid systems with binary-switches that act under autonomous switchings is studied, and the well-posedness problem (existence and uniqueness of solutions) of such systems is addressed. First, the notion of a new transition rule of the discrete state, called the switch-based transition rule, is introduced. Several differences between the behavior of solutions under this new transition rule and that under the mode-based transition rule usually used in the class of piecewise affine systems, are pointed out. Next, a sufficient condition for such a multi-modal system to be well-posed in the sense of Caratheodory is given in terms of well-posedness of bimodal systems