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    Robust stability analysis of fractional-order interval systems with multiple time delays

    , Article International Journal of Robust and Nonlinear Control ; Volume 29, Issue 6 , 2019 , Pages 1823-1839 ; 10498923 (ISSN) Mohsenipour, R ; Fathi Jegarkandi, M ; Sharif University of Technology
    John Wiley and Sons Ltd  2019
    Abstract
    This paper investigates the robust stability analysis of fractional-order interval systems with multiple time delays, including retarded and neutral systems. A bound on the poles of fractional-order interval systems of retarded and neutral type is obtained. Then, the concept of the value set and zero exclusion principle is extended to these systems, and a necessary and sufficient condition is produced for checking the robust stability of them. The value set of the characteristic equation of the systems is obtained analytically and, based on it, an auxiliary function is introduced to check the zero exclusion principle. Finally, two numerical examples are given to illustrate the effectiveness... 

    Stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters

    , Article Automatica ; Volume 49, Issue 5 , 2013 , Pages 1287-1294 ; 00051098 (ISSN) Mesbahi, A ; Haeri, M ; Sharif University of Technology
    2013
    Abstract
    This paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples  

    Decomposition and robust non-fragile stabilisation of singular time-delay systems

    , Article IET Control Theory and Applications ; Volume 12, Issue 13 , 2018 , Pages 1882-1888 ; 17518644 (ISSN) Zahedi, F ; Haeri, M ; Sharif University of Technology
    Abstract
    This study presents a new approach to decompose singular time-delay systems (STDSs) in a way that they can be transformable to normal time-delay systems (TDSs) with a lower order. Necessary and sufficient conditions are provided to determine which STDSs can be transformed to TDSs. Also, a stabilisation method is provided to stabilise the system, while the time delay in the system can belong to several distinct intervals or even everywhere. The proposed method is non-fragile towards controller parameters. This method also reveals one of the many applicable situations of the proposed decomposition. The effectiveness of the proposed method is illustrated through some examples. © 2018 The... 

    Stable regions in the parameter space of delays for LTI fractional-order systems with two delays

    , Article Signal Processing ; Volume 107 , February , 2014 , Pages 415–424 ; ISSN: 01651684 Mesbahi, A ; Haeri, M ; Sharif University of Technology
    Abstract
    This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

    BIBO stability of fractional delay systems in the parametric space of delays

    , Article International Conference on Control, Automation and Systems ; 2011 , Pages 1841-1845 ; 15987833 (ISSN) ; 9781457708350 (ISBN) Mesbahi, A ; Haeri, M ; Nasiri, H. R ; Sharif University of Technology
    2011
    Abstract
    In this work, a novel method is proposed to study the BIBO stability of a fractional delay system. The characteristic equation of a fractional delay system with some transcendental terms has infinitely many roots. Applying D-subdivision method and the Rekasius substitution divide one-dimensional parametric space of the time delay to infinite intervals with finite unstable roots. The number of unstable roots in each interval is calculated with the definition of root tendency on the boundary of each interval. Two illustrative examples are presented to confirm the proposed method results  

    Stability Analysis of Fractional Time Delayed Linear Time Invariant Systems with Infinitesimal Fractions

    , M.Sc. Thesis Sharif University of Technology Nasiri, Hamid Reza (Author) ; Haeri, Mohammad (Supervisor)
    Abstract
    Time delay generates exponential transcendental terms in characteristic equations. Subsequently, the applied methods are narrow to assess the stability map of delayed fractional-order systems with vanishing fractions. In this case, it is convenient to approximate these equations with its integer-order counterparts to design controllers or investigating features of the systems. But, delay can cause enormous differences between characteristic of these two equations. This study offers a method to survey analytically the stability of fractional-order time delayed linear time invariant systems with infinitesimal fractions. In this method, equations are transferred to an explicit expression which... 

    Decomposition of the time delay systems with one delay: The simultaneous similarity of two matrices

    , Article ELECO 2013 - 8th International Conference on Electrical and Electronics Engineering, Bursa ; 2013 , Pages 487-491 ; 9786050105049 (ISBN) Mesbahi, A ; Haeri, M ; Sharif University of Technology
    IEEE Computer Society  2013
    Abstract
    The time delay equations are frequently used to model real systems since they can describe the after-effect phenomenon. It is usually difficult to analyze the properties of time delay systems. Thus it would be beneficial to make the systems as simple as possible. For this purpose, the decomposition of the systems into some separate or cascaded sub-systems with smaller dimension is introduced as the solution of the mentioned complex task. The decomposition of the time delay systems with one delay is directly related to simultaneous similarity of two matrices. In this regard, necessary and sufficient conditions are derived for the existence of a common similar block diagonal or triangular form... 

    Oscillator Design Using Fractional Order Delayed Systems with a Minimum Order

    , M.Sc. Thesis Sharif University of Technology Allahdinian Hasaruyeh, Moein (Author) ; Haeri, Mohammad (Supervisor)
    Abstract
    The maximum number of oscillation frequencies which can be generated in a linear integer order system at the steady state is the half of its inner dimension. In this thesis, we seek the using of fractional order delayed systems with minimum order to produce maximum number of oscillation frequencies. We found a relation between the system parameters and the oscillation frequency and then adjust the system’s coefficients so that all the roots of the characteristic equation, except the roots on the imaginary axis, lie on the left-hand side of the imaginary axis. Taking into account the diagonal and triangular lower for the state space matrices of fractional order systems with one delay, we... 

    Robust controller design for discrete unstable non-minimum-phase delayed stochastic processes

    , Article International Journal of Control, Automation and Systems ; Volume 11, Issue 5 , 2013 , Pages 893-902 ; 15986446 (ISSN) Rezaei, S ; Shahrokhi, M ; Sharif University of Technology
    2013
    Abstract
    Control of unstable non-minimum-phase delayed stochastic processes is a challenging problem. In this work based on the Diophantine equation and using pole-placement technique, a discrete control scheme for such processes has been proposed. Robust stability of the suggested control structure has been shown. Advantages of the proposed scheme over the existing algorithms have been shown through computer simulations. It has been shown that performance of the proposed scheme for handling model mismatch and colored noise is superior to the previous work proposed in the literature  

    Constrained tuning of two-parameter controllers: A centroid approach

    , Article Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering ; Volume 226, Issue 5 , 2012 , Pages 685-698 ; 09596518 (ISSN) Rahimian, M. A ; Tavazoei, M. S ; Sharif University of Technology
    2012
    Abstract
    The problem of tuning a two-parameter controller has been formulated as finding the centroid of the admissible region specified by the set of constraints that the controller should satisfy. The constraints can be as general as the closed-loop system stability or they may include several requirements on various stability, sensitivity, or performance measures. The design of stabilizing proportional-derivative (PD) controllers using the centroid of the stability region in the controller parameter space is considered as a case study. To this end, analytical formulas are derived to describe the stability boundaries of a class of integrating time delay systems, the stability region of which has a... 

    Stability analysis of fractional order timedelay systems: Constructing new Lyapunov functions from those of integer order counterparts

    , Article IET Control Theory and Applications ; Volume 13, Issue 15 , 2019 , Pages 2476-2481 ; 17518644 (ISSN) Badri, V ; Tavazoei, M. S ; Sharif University of Technology
    Institution of Engineering and Technology  2019
    Abstract
    This study deals with proposing a Lyapunov-based technique for stability analysis of fractional order time-delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov-Krasovskii functionals commonly used in stability analysis of integer order time-delay systems. As a consequence for this achievement, it is revealed that the Lyapunov-Krasovskii-based stability conditions in integer order time-delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann-Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different... 

    New approach to standing phase angle reduction for power system restoration

    , Article European Transactions on Electrical Power ; Volume 12, Issue 4 , 2002 , Pages 301-307 ; 1430144X (ISSN) Ketabi, A ; Ranjbar, A. M ; Feuillet, R ; Sharif University of Technology
    2002
    Abstract
    During power system restoration, it is necessary to check the phase angle between two buses before closing circuit breakers to connect a line between them. These angles may occur across a tie line between two systems or between two connected subsystems within a system. In case of large Standing Phase Angle (SPA) difference the synchrocheck relay does not allow closing of the breaker for this line. Therefore, this excessive SPA has to be reduced before attempting to connect the line. In this paper a new and fast method for reducing SPA is presented. For this purpose, the standing phase angle difference between two specific buses is represented in terms of sensitivity factors associated with... 

    Stable regions in the parameter space of delays for LTI fractional-order systems with two delays

    , Article Signal Processing ; Volume 107 , February , 2015 , Pages 415-424 ; 01651684 (ISSN) Mesbahi, A ; Haeri, M ; Sharif University of Technology
    Elsevier  2015
    Abstract
    This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

    Asymptotic stability of linear descriptor systems with time-delay by designing delay margin

    , Article 5th International Conference on Control, Instrumentation, and Automation, ICCIA 2017 ; Volume 2018-January , 2018 , Pages 23-29 ; 9781538621349 (ISBN) Zahedi, F ; Haeri, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2018
    Abstract
    In this paper a new approach is developed to stabilize descriptor systems with time-delay, while time-delay can belong to a given interval. This approach takes the advantages of system's singularity to simplify the model and uses the so-called Rekasius substitution to compute the controller parameters in a way that the asymptotic stability of the closed-loop system in the given interval of the delay can be guaranteed. Finally, a numerical example is provided to evaluate the proposed method's effectiveness. © 2017 IEEE  

    Stability Analysis of Fractional Delay Systems in the Frequency Domain

    , Ph.D. Dissertation Sharif University of Technology Mesbahi, Afshin (Author) ; Haeri, Mohammad (Supervisor)
    Abstract
    An algebraic method is presented for assessing the bounded input bounded output (BIBO) stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. Moreover, a delay-independent BIBO-stability criterion is provided. Based on the... 

    Robust D-stability Analysis of a Class of Interval Fractional Order Systems

    , Ph.D. Dissertation Sharif University of Technology Mohsenipour, Reza (Author) ; Fathi Jegarkandi, Mohsen (Supervisor)
    Abstract
    Because of advancing fractional calculus and modeling physical phenomena by using fractional calculus more accurately than that by using integer calculus, and also existing uncertainties in models of real world systems, robust stability and performance analysis of fractional order systems are necessary. This thesis deals with the robust -stability analysis of LTI fractional order systems from kind of uncertain typical fractional order systems (UTFOS) and the robust stability analysis of LTI fractional order systems with delays from kind of uncertain retarded type systems (URTS) and uncertain neutral type systems (UNTS) with interval uncertainties. The coefficients of the numerator and the... 

    Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

    , Article Journal of Process Control ; Vol. 24, issue. 9 , 2014 , pp. 1489-1494 Mesbahi, A ; Haeri, M ; Sharif University of Technology
    Abstract
    A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method  

    Necessary and sufficient conditions for BIBO-stability of some fractional delay systems of neutral type

    , Article IEEE Transactions on Automatic Control ; Volume 56, Issue 1 , 2011 , Pages 125-128 ; 00189286 (ISSN) Akbari Moornani, K ; Haeri, M ; Sharif University of Technology
    2011
    Abstract
    In this note, bounded-input bounded-output (BIBO)-stability of a large class of neutral type fractional delay systems is investigated. Necessary and sufficient conditions of BIBO-stability are presented for the intended class of systems (the sufficient conditions have been provided for a more general case in the previous studies). Two lemmas are provided for checking a prerequisite imposed on the considered class of systems. Finally, two numerical examples are given to illustrate the obtained results  

    On robust stability of LTI fractional-order delay systems of retarded and neutral type

    , Article Automatica ; Volume 46, Issue 2 , 2010 , Pages 362-368 ; 00051098 (ISSN) Akbari Moornani, K ; Haeri, M ; Sharif University of Technology
    2010
    Abstract
    This paper deals with the analysis of robust BIBO-stability of LTI fractional order delay systems in the presence of real parametric uncertainties. Two large classes of these systems, namely retarded and neutral types, are considered. Two theorems are given to check the robust BIBO-stability of these two families of fractional order systems. One of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type. Furthermore, upper and lower bounds (cutoff frequencies) are provided for drawing the value sets. To illustrate the results, two numerical examples are presented  

    Stability of neutral type fractional delay systems and its relation with stability of timedelay and discrete systems

    , Article IET Control Theory and Applications ; Volume 10, Issue 18 , 2016 , Pages 2482-2489 ; 17518644 (ISSN) Mesbahi, A ; Haeri, M ; Sharif University of Technology
    Institution of Engineering and Technology  2016
    Abstract
    The bounded-input bounded-output stability of fractional delay systems of neutral type is investigated in this study. The proposed method calculates the number of unstable poles of the system for each delay value. All time-delay intervals in time-delay space where system is stable are precisely determined. The stability of systems with not only indefinitely large values of time-delay, but also with multiple poles on the imaginary axis has been studied. The proposed method is employed for investigating the stability of a fractional delay system when its fractional orders approach to the integer numbers or zero. It is proved that simple case of neutral types and time-delay systems have the...