On Lower Bound of SSV with Phase-Informed Uncertainty

• Main Authors: Ou, Jih Hwa, 歐濟華
• Other Authors: Lee, Li
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/32525022089255389786

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.