@book{4200098250c84029a4d924801f6a17fd,

title = "Characterization of well-posedness of piecewise linear systems",

abstract = "One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed.",

keywords = "MSC-90C33, MSC-93A30, EWI-3295, IR-65664, MSC-93B99",

author = "J.I. Imura and {van der Schaft}, Arjan",

note = "Imported from MEMORANDA",

year = "1998",

language = "Undefined",

series = "Memorandum / Department of Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1475",

}