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Robust Stability Analysis of a Family of Fractional Order Systems with Structured Real Parametric Uncertainties

Akbari Moornani, Kamran | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40983 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Haeri, Mohammad
  7. Abstract:
  8. Transfer functions of some important classes of infinite-dimensional LTI systems contain semi-polynomials in fractional powers of Laplace variable , possibly in combination with delay terms or exponentials of fractional powers of . They can be observed in many systems and subjects such as biological systems, distributed parameter systems and heat flowing phenomena. Some appropriate theorems relevant to the subject of BIBO-stability are available for a large class of such systems, though many difficulties arise in applying them analytically. In this work, some parameters of the transfer functions of such systems (e.g., the coefficients of the numerators and denominators) are considered as continuous functions of the vector of real uncertain parameters, and the robust BIBO-stability of the resulting family of systems is studied. The concept of “value set” plays a basic role in this subject for rational systems. This research employs the same concept for the topic of the robust BIBO-stability of the families of fractional order systems. This way, some relevant theorems and concepts are generalized, including zero exclusion condition theorem, Kharitonov’s theorem, robust stability testing function, edge theorem, robustness margin, etc. To be certain about the correctness of these generalizations, one should impose some prerequisites on the intended families; of course, these restrictions are considered so that the studied materials are applicable to an extensive field of the families of fractional order systems). In summary, this research provides some appropriate procedures for robust BIBO-stability analysis of some large classes of families of fractional order systems with structured real parametric uncertainties through generalizing some existing results in the field of rational systems to the field of fractional order systems.
  9. Keywords:
  10. Fractional Order System ; Structured Real Parametric Uncertainties ; Robust Bounded-Input Bounded-Output (BIBO)Stability ; Value Set ; Zero Exclusion Condition Theorem ; Kharitonoves Theorem ; Edge Theorem

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