| Summary: | 碩士 === 國立中山大學 === 電機工程研究所 === 84 === Besides stability and performance, the two main goals of
control system design framework, the consideration of e-
xistence of uncertainty in almost all practical systems makes
robustness become another important issue in cont- rol theory.
Within many well-established theories for r- obustness study,
the structured singular value theory,b- riefly called the μ-
theory,proposed by Doyle in 1982 h- as been proven a powerful
tool for the analysis of robu- st stability and robust
performance.Several μ values a- nd the related properties have
been developed for diffe- rent uncertainty models, e.g.,
complex μ, real μ, mix- ed μ, and phase μ, etc. In the
thesis, we study the p- roperties of lower bound of μ when, in
the block diago- nal structure, the repeated scalar
uncertainties contain phase information bounded by a symmetric
cone. First, we extend the characterization of lower bounds
on complex and mixed μs to the phase μ case, and derive a
main r- esult for equality between the phase μ and its
refined lower bound. This result, when specifying the phase
bou- nds properly, leads to the corresponding complex- and m-
ixed-μ results. In view of the difficulty in solving t- he
refined lower bound directly, some additional proper- ties
which are essential to developing algorithms to co- mpute a
tight lower bound on phase μ are then derived. Finally, we
suggest some interesting and related topics as the possible
future research directions.
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