Conditions on Fractional-order LTI Systems to be Negative Imaginary

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Neshat Taherzadeh, Khashayar | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52441 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Tavazoei, Mohammad Saleh
Abstract:
In this thesis, we derive the analytic condition that linear time invariant fractional order system being positive real. Also, by inspiration of positive real condition, we derive the analytic condition for linear time invariant fractional order system that their imaginary part of frequency response being negative. Intended conditions for single input single output systems are derived in the form of necessary conditions in one way and derived in the form of sufficient conditions in another way. However, intended conditions in multiple input multiple output are just derived in the form of sufficient conditions. Furthermore, an upper band for phase of oustaloup approximation frequency response is obtained and its usage in deriving indented conditions have been explained. In the end of any chapters, usefull examples are shown how necessary conditions and sufficient conditions are conservative. Ultimately, future works that can persue this thesis are suggested
Keywords:
Negative Imaginary Systems ; Positive Real Systems ; Fractional Order System ; Oustaloup Approximation ; Linear Matrix Inequality (LMI)

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