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In this paper, we deal with the well-posedness (in the sense of existence anduniqueness of solutions) and nature of solutions for discontinuous bimodalpiecewise affine systems in a differential inclusion setting. First, we showthat the conditions guaranteeing uniqueness of Filippov solutions in thecontext of general differential inclusions are quite restrictive when appliedto bimodal piecewise affine systems. Later, we present a set of necessary andsufficient conditions for uniqueness of Filippov solutions for bimodalpiecewise affine systems. We also study the so-called Zeno behavior(possibility of infinitely many switchings within a finite time interval) forFilippov solutions.

On the existence, uniqueness and nature of Caratheodory and Filippov solutions for bimodal piecewise affine dynamical systems