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Stabilization of Linear and Nonlinear Differential Inclusions Considering Fractional and Integer order Derivatives

Abooee, Ali | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47932 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineerign
  6. Advisor(s): Haeri, Mohammad
  7. Abstract:
  8. First, stabilization problem of an integer order-nonlinear differential inclusion (IO-NDI) in the form of tracking problem is investigated and discussed while control inputs are subjected to the sector and dead-zone nonlinearities. Based on two the well-known theorems, the mentioned differential inclusion is modeled by a nonlinear system possessing polytopic uncertainties. For tackling the mentioned problem, sliding mode control (SMC) approach is applied and developed. Second, two issues including stability analysis and stabilization problem of a fractional order-linear differential inclusion (FO-LDI) are studied for both fractional order derivatives and separately. For solving these problems, the mentioned differential inclusion is described by a linear time invariant-fractional order system (LTI-FOS) along with polytopic and interval uncertainties. Some sufficient conditions in the form of linear matrix inequalities (LMIs) are obtained for handling two the mentioned problems. Third, stabilization problem of a fractional order-nonlinear differential inclusion (FO-NDI) in the presence of bounded disturbances is investigated while control inputs are subjected to the sector and dead-zone nonlinearities. For achieving the stabilization goal, the mentioned differential inclusion is modeled by a nonlinear fractional order system (NFOS) and the adaptive-sliding mode control method is applied.Forth, stabilization problem for the Lur’e inclusions in the form of synchronization aim is studied. For synchronization problem, two master and slave Lur’e inclusions are considered where their parameters are unknown and their control inputs are subjected to the sector nonlinearities. Based on the direct Lyapunov method, control inputs of slave Lur’e inclusion are designed to synchronize all state variables of two mentioned Lur’e inclusions
  9. Keywords:
  10. Linear Matrix Inequality (LMI) ; Lur'e Systems ; Polytopic Uncertainty ; Stability Analysis ; Interval Uncertainty ; Robust Asymptotic Stabilization ; Sector Nonlinearities ; Dead-Zone Nonlinearities ; Integer Differential Inclusions

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