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Comments on "stability analysis of a class of nonlinear fractional-order systems"
, Article IEEE Transactions on Circuits and Systems II: Express Briefs ; Volume 56, Issue 6 , 2009 , Pages 519-520 ; 15497747 (ISSN) ; Sharif University of Technology
2009
Abstract
It has been pointed out that the numerical simulation results presented in the above paper are not consistent with reality. The reason for this inconsistency has analytically been clarified in this note. © 2009 IEEE
Stability Analysis of Fractional Order Systems Described in Lur'e Structure
,
M.Sc. Thesis
Sharif University of Technology
;
Tavazoei, Mohammad Saleh
(Supervisor)
Abstract
Most of the real-world systems can be modeled as closed loop systems which are made up of a LTI subsystem in the forward path and a memoryless nonlinear subsystem in the feedback path. Such systems are called “Lur’e systems”, the name of the first who introduced these systems. Because of the generality and the wide applicability of this type of systems, studying the stability of them has been notable and interesting to many scientists for a long time. Meanwhile, in recent decades, many scientists in physics and engineering sciences have been interested in applications of the fractional order systems and as a result focused on studying the features of the fractional order systems. An...
On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment
, Article Applied Mathematical Modelling ; Vol. 38, issue. 3 , 2014 , pp. 961-973 ; ISSN: 0307904X ; Salarieh, H ; Alasty, A ; Meghdari, A ; Sharif University of Technology
Abstract
In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the...
Adaptive consensus tracking for fractional-order linear time invariant swarm systems
, Article Journal of Computational and Nonlinear Dynamics ; Vol. 9, issue. 3 , 2014 ; ISSN: 15551415 ; Tavazoei, M. S ; Sharif University of Technology
Abstract
This paper presents an adaptive controller to achieve consensus tracking for the fractional-order linear time invariant swarm systems in which the matrices describing the agent dynamics and the interactive dynamics between agents are unknown. This controller consists of two parts: an adaptive stabilizer and an adaptive tracker. The adaptive stabilizer guarantees the asymptotic swarm stability of the considered swarm system. Also, the adaptive tracker enforces the system agents to track a desired trajectory while achieving consensus. Numerical simulation results are presented to show the effectiveness of the proposed controller. Copyright
Time response analysis of fractional-order control systems: A survey on recent results
, Article Fractional Calculus and Applied Analysis ; Vol. 17, Issue. 2 , June , 2014 , pp. 440-461 ; ISSN: 13110454 ; Sharif University of Technology
Abstract
The aim of this paper is to provide a survey on the recently obtained results which are useful in time response analysis of fractional-order control systems. In this survey, at first some results on error signal analysis in fractional-order control systems are presented. Then, some previously obtained results which are helpful for system output analysis in fractional-order control systems are summarized. In addition, some results on the analysis of the control signal and the system response to the load disturbances in fractional-order control systems are reviewed
Phase plane characteristics of marginally stable fractional order systems
, Article Nonlinear Science and Complexity ; 2011 , Pages 293-301 ; 9789048198832 (ISBN) ; Haeri, M ; Tavazoei, M. S ; Sharif University of Technology
Springer Netherlands
2011
Abstract
When an integer order linear time invariant system possesses unrepeated pure imaginary poles it can generate oscillatory response which is represented by invariant closed contours in the phase plane. In linear time invariant fractional order systems with the same property, due to their special characteristics, this behavior will be more complicated and the contours would not be invariant. In this paper we will investigate the behavior of fractional order systems under such conditions
Comments on " Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control" [Commun Nonlinear Sci Numer Simulat 2010;15:3754-3762]
, Article Communications in Nonlinear Science and Numerical Simulation ; Volume 16, Issue 6 , June , 2011 , Pages 2656-2657 ; 10075704 (ISSN) ; Beheshti, M. T. H ; Tavazoei, M. S ; Sharif University of Technology
2011
Abstract
In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754-3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification
On the general Kalman filter for discrete time stochastic fractional systems
, Article Mechatronics ; Volume 23, Issue 7 , 2013 , Pages 764-771 ; 09574158 (ISSN) ; Salarieh, H ; Alasty, A ; Meghdari, A ; Sharif University of Technology
2013
Abstract
In this paper the derivation of Kalman filter for discrete time-stochastic fractional system is investigated. Based on a novel cumulative vector form model for fractional systems, a general Kalman filter is introduced. The validity of the proposed method has been compared with a previously presented method via simulation results. It is shown that this method can be better applied for discrete time stochastic fractional systems with slower dynamics
Toward searching possible oscillatory region in order space for nonlinear fractional-order systems
, Article Journal of Computational and Nonlinear Dynamics ; Vol. 9, issue. 2 , 2014 ; Sharif University of Technology
Abstract
Finding the oscillatory region in the order space is one of the most challenging problems in nonlinear fractional-order systems. This paper proposes a method to find the possible oscillatory region in the order space for a nonlinear fractional-order system. The effectiveness of the proposed method in finding the oscillatory region and special order sets placed in its boundary is confirmed by presenting some examples
The effect of fractional order on oscillatory behavior of scalar fractional delay systems of neutral type
, Article IFAC Proceedings Volumes (IFAC-PapersOnline) ; February , 2013 , Pages 480-485 ; 14746670 (ISSN); 9783902823274 (ISBN) ; Haeri, M ; Sharif University of Technology
2013
Abstract
The undamped oscillations of a scalar fractional neutral system are studied in this paper. For this purpose, it is proved that this kind of systems can have the oscillatory behavior. The necessary and sufficient condition is proposed to determine that there exists a delay value for which the system oscillates. The frequency, amplitude and required delay for the undamped oscillations depend on the fractional order. However, the behavior of dependencies is not specified. Indeed, when the system has oscillatory behavior, it is bounded-input bounded-output stable for delay less than the required delay. Moreover, when the order is approaching to an integer value, the necessary and sufficient...
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) ; 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
Comments on chaotic characteristics analysis and circuit implementation for a fractional-order system
, Article IEEE Transactions on Circuits and Systems I: Regular Papers ; Volume 62, Issue 1 , 2015 , Pages 329-332 ; 15498328 (ISSN) ; Sharif University of Technology
Abstract
In this note, it is shown that some of the results reported in the above titled paper on the behavior analysis of a fractional order system are not consistent with reality. To support this claim, theoretical justifications and numerical results are presented. Also, it is analytically explained that why such inconsistencies have been occurred in the aforementioned paper
Constrained swarm stabilization of fractional order linear time invariant swarm systems
, Article IEEE/CAA Journal of Automatica Sinica ; Volume 3, Issue 3 , 2016 , Pages 320-331 ; 23299266 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
Abstract
This paper deals with asymptotic swarm stabilization of fractional order linear time invariant swarm systems in the presence of two constraints: the input saturation constraint and the restriction on distance of the agents from final destination which should be less than a desired value. A feedback control law is proposed for asymptotic swarm stabilization of fractional order swarm systems which guarantees satisfying the above-mentioned constraints. Numerical simulation results are given to confirm the efficiency of the proposed control method
A proof for non existence of periodic solutions in time invariant fractional order systems
, Article Automatica ; Volume 45, Issue 8 , 2009 , Pages 1886-1890 ; 00051098 (ISSN) ; Haeri, M ; Sharif University of Technology
2009
Abstract
The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo's definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems. © 2009 Elsevier Ltd. All rights reserved
Stabilization of unstable fixed points of chaotic fractional order systems by a state fractional PI controller
, Article European Journal of Control ; Volume 14, Issue 3 , 2008 , Pages 247-257 ; 09473580 (ISSN) ; Haeri, M ; Sharif University of Technology
Lavoisier
2008
Abstract
This paper presents a new method to control chaos in fractional order systems based on the fractional control theory. The proposed controller is a fractional P1 (PIα) controller and can locally stabilize unstable equilibrium points of a class of chaotic fractional order systems. Using the ideas available in the chaos control methods such as On-Grebogi-Yorke (OGY), this local stabilization can be extended to the global stabilization. The controller has simple structure and its parameters can be determined by pole placement technique. To illustrate its capability, the proposed controller is applied to control chaos in the fractional order unified system. Numerical simulations confirm the...
Fragility Analysis of Fractional-Order PID Controllers
, M.Sc. Thesis Sharif University of Technology ; Tavazoei, Mohammad Saleh (Supervisor)
Abstract
This thesis, argues on recently published methods for tuning of fractional PID controllers. Proposed algorithms provided tuning rules to achieve design objective such as, phase margin, gain cross-over frequency and zero derivative of the phase versus frequency at cross-over frequency. Third constraint imposed to reach high robustness to gain loop variation for controller. Tuning rules attained by consideration on the insensitivity of both stability and desired performance to the system parameter variations, but not on own controller. At the present paper, based on geometric approach, fragility analysis of the fractional-order of some types of PID setting for considering the robustness of the...
On the general Kalman filter for discrete time stochastic fractional systems
, Article Mechatronics ; Volume 23 , Issue 7 , October , 2013 , pp. 764-771 ; ISSN: 09574158 ; Salarieh, H ; Alasty, A ; Meghdari, A ; Sharif University of Technology
Abstract
In this paper the derivation of Kalman filter for discrete time-stochastic fractional system is investigated. Based on a novel cumulative vector form model for fractional systems, a general Kalman filter is introduced. The validity of the proposed method has been compared with a previously presented method via simulation results. It is shown that this method can be better applied for discrete time stochastic fractional systems with slower dynamics
Algebraic conditions for monotonicity of magnitude-frequency responses in all-pole fractional order systems
, Article IET Control Theory and Applications ; Volume 8, Issue 12 , 2014 , Pages 1091-1095 ; ISSN: 17518644 ; Sharif University of Technology
Abstract
This study deals with the investigation of the magnitude-frequency responses of all-pole fractional order systems in the viewpoint of extrema existence in these responses. In this investigation, a sufficient algebraic condition, two necessary algebraic conditions, and a necessary and sufficient algebraic condition are obtained to guarantee the non-existence of extrema in the magnitude-frequency response of all-pole fractional order systems. Some examples are presented to show the effectiveness of the results of the paper
Study on control input energy efficiency of fractional order control systems
, Article IEEE Journal on Emerging and Selected Topics in Circuits and Systems ; Volume 3, Issue 3 , July , 2013 , Pages 475-482 ; 21563357 (ISSN) ; Haeri, M ; Tavazoei, M. S ; Sharif University of Technology
2013
Abstract
Control input energy efficiency is an important issue which should be considered in designing any control system. Due to the importance of this subject, in the present paper fractional order control systems are studied in the viewpoint of control input energy efficiency. In this study, the divergent terms of the control input energy function of fractional order control systems are obtained. It is shown that these terms have a significant role in the amount of the energy injected to the plant by the controller. Finally, two examples are provided to demonstrate the usefulness of the presented results in the paper
On type number concept in fractional-order systems
, Article Automatica ; Volume 49, Issue 1 , January , 2013 , Pages 301-304 ; 00051098 (ISSN) ; Sharif University of Technology
2013
Abstract
In this note, the type number concept is defined for fractional-order systems. Based on this definition, it is shown that fractional-order systems having type numbers more than 1 can not track some classes of reference inputs without any overshoot