Sharif Digital Repository

This paper is devoted to analysis of undamped oscillations generated by fractional order linear time invariant (LTI) systems. At first, the trajectories of marginally stable commensurate order systems are investigated. It is verified that we can not use the time-independent phase flow concept for this kind of systems. Also, the differences with the integer order case are highlighted. Then, it is shown that we can determine the Q-norm of the limit sets of a trajectory for these systems based on the Q-norm of the initial condition. Some numerical examples are brought to confirm the achievements of the paper  

This paper studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the use of the paper results  

In this paper, a class of the direct methods for discretization of fractional order transfer functions is studied in the sense of stability preservation. The stability boundary curve is exactly determined for these discretization methods. Having this boundary helps us to recognize whether the original system and its discretized model are the same in the sense of stability. Finally, some illustrative examples are presented to evaluate achievements of the paper  

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... 

This paper deals with a fractional calculus based control strategy for chaos suppression in the 3D chaotic systems. It is assumed that the structure of the controlled chaotic system has only one control input. In the proposed strategy, the controller has three tuneable parameters and the control input is constructed as fractional-order integration of a linear combination of linearized model states. The tuning procedure is based on the stability theorems in the incommensurate fractional-order systems. To evaluate the performance of the proposed controller, the design method is applied to suppress chaotic oscillations in a 3D chaotic oscillator and in the Chen chaotic system. © 2008 Springer... 

In this paper, the frequency domain-based numerical methods for simulation of fractional order systems are studied in the sense of stability preservation. First, the stability boundary curve is exactly determined for those methods. Then, this boundary is analyzed and compared with an accurate (ideal) boundary in different frequency ranges. Also, the critical regions in which the stability does not preserve are determined. Finally, the analytical achievements are confirmed via some numerical illustrations. © 2008 Society for Industrial and Applied Mathematics  

This paper is devoted to the analysis of fractional order Van der Pol system studied in the literature. Based on the existing theorems on the stability of incommensurate fractional order systems, we determine parametric range for which a fractional order Van der Pol system with a specific order can perform as an undamped oscillator. Numerical simulations are presented to support the given analytical results. These results also illuminate a main difference between oscillations in a fractional order Van der Pol oscillator and its integer order counterpart. We show that contrary to integer order case, trajectories in a fractional Van der Pol oscillator do not converge to a unique cycle. © 2009... 

Let γs′ (G) be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n (n ≥ 2), γs′ (G) ≥ 1. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that γs′ (G) ≤ - frac(m, 6) | V (G) |. Also for every two natural numbers m and n, we determine γs′ (Km, n), where Km, n is the complete bipartite graph with part sizes m and n. © 2008 Elsevier B.V. All rights reserved  

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented. © 2008 IEEE  

Using multiple antennas at the transmit and receive sides of a passive radar brings both the benefits of MIMO radar and passive radar. However one of the obstacles arisen in such configuration is the receive antennas placement in proper positions so that the radar performance is improved. Here we just consider the case of positioning one receiver among multiple illuminators of opportunity. Indeed it is a start for the solution of optimizing the geometry of the multiple receivers in a passive radar  

SbCl3 supported on montmorillonite K-10 is an efficient catalyst for the ring opening of epoxides with aromatic amines under solvent-free conditions and microwave irradiation to give the corresponding b-amino alcohols in high yields with high regioselectivity  

In this paper, we consider an integrated sensing and communication (ISAC) system with wireless power transfer (WPT) where an unmanned aerial vehicle (UAV)-based radar serves a group of energy-limited communication users in addition to its sensing functionality. In this architecture, the radar senses the environment in phase 1 (namely sensing phase) and mean-while, the communications users (nodes) harvest and store the energy from the radar transmit signal. The stored energy is then used for information transmission from the nodes to UAV in phase 2, i.e., uplink phase. Performance of the radar system depends on the transmit signal as well as the receive filter; the energy of the transmit... 

One of the important obstacles in MIMO (Multiple Input Multiple Output) radars is the issue of designing proper transmit signals. Indeed, the capability of signal design is a significant advantage in MIMO radars, through which, the system can achieve much better performance. Many different aspects of this performance improvement have been considered yet, and the transmit signals have been designed to attain such goal, e.g., getting higher SNR or better detector's performance at the receiver. However, an important tool for evaluating the radar's performance is its ambiguity function. In this paper, we consider the problem of transmit signal design, in order to optimize the ambiguity function... 

Two gains play key roles in recently developed MIMO wireless communication systems: "spatial diversity" gain and "spatial multiplexing" gain. The diversity gain refers to the capability to decrease the error rate of the MIMO channel, while the multiplexing gain implicitly refers to the amount of increase in the capacity of the MIMO channel. It has been shown that there is a fundamental tradeoff between these two types of gains, meaning interplay between increasing reliability (via an increase in the diversity gain) and increasing data rate (via an increase in the multiplexing gain). On the other hand, recently, MIMO radars have attracted much attention for their superior ability to enhance... 

It is a well known fact that using multiple antennas at transmit and receive sides improves the detection performance. However, in such multiple-input multiple-output (MIMO) configuration, proper positioning of transmitters and receivers is a big challenge that can have significant influence on the performance of the overall system. In addition, determining the power of each transmitter under a total power constraint is a problem that should be solved in order to enhance the performance and coverage of such a system. In this paper, we design the Neyman-Pearson detector under the Rayleigh scatter model and use it to introduce a criterion for the antenna placement at both transmit and receive... 

There has been much interest, recently, towards exploiting the Multiple-Input Multiple-Output (MIMO) technique in radar. It is shown that using multiple antennas at transmit and receive sides can improve the performance of the system. However, in order to analyze the system's performance, its ambiguity function, i.e. the ambiguity function of a MIMO radar, is needed to be defined. In this paper, beginning from the information theoretic definitions, we derive such function, specifically for a MIMO radar with widely separated antennas  

By combining the two ideas of MIMO (Multiple Input Multiple Output) and PCL (Passive Coherent Location) in radar, one can achieve the advantages of both recently developed techniques simultaneously. While using multiple antennas at the receive side provides a spatial diversity of the object to be detected, using multiple illuminators of opportunity, most importantly, makes the radar covert to the interceptors. One obstacle in such MIMO configuration is choosing the positions of the receive antennas. In this paper, after analyzing the Neyman-Pearson detector for the DVB-T based PCL, we introduce the probability of missed detection as a criterion to place the receive antenna. Here, we only... 

One of the most important obstacles in passive radar applications is removing the direct signal from the target channel. Otherwise, week echoes from the targets in the target channel would be ignored due to the limited dynamic range of the system. One of the most effective techniques in this field is using adaptive filters. In this paper various adaptive filters are introduced and their performances are shown and compared