SICE Journal of Control, Measurement, and System Integration
Online ISSN : 1884-9970
Print ISSN : 1882-4889
ISSN-L : 1882-4889
Note on Well-Posedness and Separator-Type Robust Stability Theorem of LTI Systems
Tomomichi HAGIWARA
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2012 Volume 5 Issue 3 Pages 169-174


This paper is concerned with the well-posedness (in the classical sense) and robust stability analysis of linear time-invariant (LTI) systems. Among approaches to robust stability analysis of LTI systems is the one based on the separator-type robust stability theorem derived through the topological separation notion. This paper first shows that the well-posedness assumption underlying this theorem, which has been considered to be essential in the discrete-time case, can actually be removed completely. Some arguments and an example are further provided, suggesting that removing such an assumption is indeed a nontrivial task. Relevant aspects are also discussed about well-posedness of uncertain systems through the systematic arguments underlying the construction of such an example, both in the discrete-time and continuous-time cases.

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© 2012 The Society of Instrument and Control Engineers
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