Abstract
This chapter consists primarily of some background material, with the selection of topics being dictated by our later needs. We introduce some notation and definitions that will be used throughout the book, recall some definitions and properties of semigroup operators and infinitesimal generators, and present some fundamental results on the existence and uniqueness of solutions of a differential equation. We also recall some basic definitions and results on continuous-time Markov chains with finite state space and introduce the spaces that are appropriate for our approach. Finally, we show some important auxiliary results regarding the stability of some operators and recall some basic facts regarding linear matrix inequalities.
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Costa, O., Fragoso, M., Todorov, M. (2013). A Few Tools and Notations. In: Continuous-Time Markov Jump Linear Systems. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34100-7_2
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DOI: https://doi.org/10.1007/978-3-642-34100-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34099-4
Online ISBN: 978-3-642-34100-7
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