Sharif Digital Repository

This paper deals with the existence and the characteristics of the limit cycles in the fractional-order Arneodo system. The analysis is done using the describing function method. Our focus is on a special case where two limit cycles exist. The parametric range for the case of interest is derived, and the frequency and the amplitude of the oscillation are predicted. Numerical simulation results are presented to further demonstrate the reliability of the analysis  

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  

Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd  

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  

In this paper, for one-dimensional stochastic linear fractional systems in terms of the Riemann-Liouville fractional derivative, the optimal control is derived. It is assumed that the state is completely observable and all the information regarding this is available. The formulation leads to a set of stochastic fractional forward and backward equation in the Riemann-Liouville sense. The proposed method has been checked via some numerical simulations which show the effectiveness of the fractional stochastic optimal algorithm  

This paper deals with the problem of designing the PI λDμ-type controllers for minimum-phase fractional systems of rational order. In such systems, the powers of the Laplace variable, s, are limited to rational numbers. Unlike many existing methods that use numerical optimisation algorithms, the proposed method is based on an analytic approach and avoids complicated numerical calculations. The method presented in this paper is based on the asymptotic behaviour of fractional algebraic equations and applies a delicate property of the root loci of the systems under consideration. In many cases, the resulted controller is conveniently in the form of P, Iλ, PDμ or PIλDμ. Four design examples are... 

This study deals with the properties of magnitude-frequency responses in fractional order systems. Using Phragmén-Lindelöf theorem in complex analysis, it is shown that the supremum of the magnitude-frequency response of a fractional system with a commensurate order less than one cannot be greater than that of its integer order bounded-input, bounded-output stable counterpart. Further results are also obtained on magnitude-frequency response of stable/unstable fractional order systems. Moreover, it is found that the supremum (infimum) of the magnitude-scaling frequency of the family of fractional order systems having a fixed structure and different orders in the range (0, 2) is a piecewise... 

This paper deals with the identification of fractional-order systems through orthogonal rational functions. Fractional systems are characterized by their non-exponential aperiodic multimodes; therefore, fractional orthogonal rational functions provide better approximating models with fewer parameters. In spite of the fact that the Laguerre-based model is simple, it is, to some extent, deficient at high frequencies. Motivated by this objective, the use of a Legendre basis which has progressive pole locations and can be expected to perform better at high frequencies is studied  

In this Letter, based on the stability theorem in fractional differential equations, a necessary condition is given to check existence of double scroll attractor in a fractional-order system. Numerical simulations are presented to evaluate accuracy of this condition in fractional-order Chen and Lü systems. Also, we show that using frequency domain approximation in the numerical simulations of fractional systems may result in wrong consequences. For example, this approximation can numerically demonstrate chaos in the non-chaotic fractional-order systems. Unfortunately, this mistake has occurred in the recent literature that found the lowest-order chaotic systems among fractional-order... 

Systemic inflammation biomarkers have been associated with risk of cardiovascular morbidity and mortality. We aimed to clarify associations of acute exposure to particulate matter (PM10(PM < 10 μm), PM2.5-10(PM 2.5–10 μm), PM2.5(PM < 2.5 μm), PM1-2.5(PM 1–2.5 μm), and PM1 (PM < 1 μm)) with systemic inflammation using panels of elderly subjects and healthy young adults. We followed a panel of 44 nonsmoking elderly subjects living in a retirement home and a panel of 40 healthy young adults living in a school dormitory in Tehran city, Iran from May 2012 to May 2013. Blood biomarkers were measured one every 7–8 weeks and included white blood cells (WBC), high sensitive C-reactive protein...