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Robust Stability Analysis of Uncertain LTI Distributed-Order Systems

Taghavian, Hamed | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49150 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. Distributed order dynamic systems are studied in this thesis. These systems incorporate distributed order operators to describe physical phenomena that naturally occur in diffusion, relaxation and viscoelasticity. Hence, the exact solutions of distributed order system of differential equations are derived analytically which are described by what we later call distributed order mittag-leffler functions. Then robust stability of distributed order LTI continuous time systems with uncertain weight functions and dynamic matrices is investigated and some sufficient conditions for stability/instability are introduced in this matter. Also, after discussing some of the properties of stability boundary curves associated with these systems, Lagrange inversion theorem is utilized to produce some conservative curves which gives some more useful sufficient conditions of stability/instability. It is also proved that just like classical systems, asymptotical stability and BIBO stability of these systems rely on the same conditions. Also, distributed order LTI discreet time systems are introduced by discretizing the primary equations, which are accompanied by a comprehensive stability discussion. Subsequently, we head for distributed order nonlinear non-autonomous systems study, and extend Lyapuno’s direct method accordingly. Needless to say, there are a lot of physical phenomena which lead to fractional order models with incommensurate orders when modelled accurately. These systems are considered as special cases of distributed order systems with impulsive weight functions. Therefore, robust stability of them is studied finally, in the rather unprecedented case that all fractional orders, coefficients and dynamic matrix are uncertain and subject to some perturbations, which results in some simple robust stability conditions eventually
  9. Keywords:
  10. Distributed Order Systems ; Robust Stability ; Uncertainty ; Lyapunov Stability ; Stability Analysis ; Incommensurate Orders

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