Modeling perspectives of hybrid systems and network systems

Abstract

This article presents two topics, i.e., well-posedness of piecewise affine systems, and model reduction of network systems. The well-posedness problem, i.e., the problem of existence and uniqueness of solutions, of hybrid systems is one of the fundamental research topics, which the first author has collaborated with Prof. Arjan van der Schaft in 1998. Some results are revisited by focusing on the class of bimodal piecewise affine systems. The latter discusses the most recent topic that both Arjan and the first author have common interest in. In particular, the clustering-based H∞− and H2-model reduction approaches of large-scale network systems, which have been independently developed by the authors, are represented in a unified way.