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    Canards in Complex Oscillatory Systems

    , M.Sc. Thesis Sharif University of Technology Naghdabadi, Zahra (Author) ; Razvan, Mohammad Reza (Supervisor)
    Abstract
    Canard, first observed in Van der Pol oscillations, is a typical phenomenon in oscillatory systems. Canard is also observed in many oscillatory systems such as electrical circuits and neurons. In many fields of science and engineering there are complex oscillations that exhibit canard for certain values of parameters. These three dimensional systems exhibit complex oscillatory behavior never observed in two dimensional dynamics. Some of these systems are chaotic for certain parameter values. It seems than in oscillatory systems canards can make complex behavior. Several methods such as the singular perturbation theory have been used to study this complexity. In this project, we study canard... 

    Maximum number of frequencies in oscillations generated by fractional order LTI systems

    , Article IEEE Transactions on Signal Processing ; Volume 58, Issue 8 , May , 2010 , Pages 4003-4012 ; 1053587X (ISSN) Tavazoei, M. S ; Haeri, M ; Siami, M ; Bolouki, S ; Sharif University of Technology
    2010
    Abstract
    In this paper, relation between the inner dimension of a fractional order LTI system and the maximum number of frequencies which exist in oscillations generated by the system is investigated. The considered system is defined in pseudo state space form and the orders of its involved fractional derivatives are rational numbers between zero and one. First, an upper bound is derived for the maximum number of frequencies. Then, using the restricted difference bases concept, a new method is introduced to design a multifrequency oscillatory fractional order system. Finally, based on the proposed method some lower bounds are derived for the maximum number of frequencies obtainable in solutions of a... 

    Backstepping boundary control for unstable second-order hyperbolic PDES and trajectory tracking

    , Article Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, 30 August 2009 through 2 September 2009 ; Volume 4, Issue PART C , August , 2010 , Pages 1787-1792 ; 9780791849019 (ISBN) Vatankhah, R ; Sadeghian, H ; Abediny, M ; Alasty, A ; Sharif University of Technology
    2010
    Abstract
    In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated... 

    Backstepping boundary control for unstable second-order hyperbolic PDEs and trajectory tracking

    , Article Proceedings of the ASME Design Engineering Technical Conference, 30 August 2009 through 2 September 2009 ; Volume 4, Issue PARTS A, B AND C , 2009 , Pages 1787-1792 ; 9780791849019 (ISBN) Vatankhah, R ; Abediny, M ; Sadeghian, H ; Alasty, A ; Design Engineering Division and Computers in Engineering Division ; Sharif University of Technology
    Abstract
    In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated...