On well-posedness of piecewise affine bimodal dynamical systems
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KünyeThuan, L. Q., & Çamlıbel, M. K. (2010). On well-posedness of piecewise affine bimodal dynamical systems. In 19th International Symposium on Mathematical Theory of Networks and Systems (pp. 503-510). Budapest: ELTE and MTA SZTAKI.
The theory of differential inclusions provides certain sufficient conditons for the uniqueness of Filippov solutions such as one-sided Lipschitzian property or maximal monotone condition. When applied to piecewise affine dynamical systems, these conditions impose rather strong conditions. In this paper, we provide less restrictive conditions for uniqueness of Filippov solutions for the bimodal piecewise affine systems.