Sharif Digital Repository

In this paper, we present sufficient conditions to address a larger class of digraphs, including balanced ones, whose members' Laplacian (L) makes L 1L + LTL1 to be positive semi-definite, where L1 is the Laplacian associated with a fully connected equally-edged weighted graphs. This property can be later utilized to introduce an appropriate energy function for stability analysis of flocking algorithms in a larger class of networks with switching directed information flow. Also, some of their properties are investigated in the line of matrix theory and graph theory  

The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneouslyvanishing quantum discord provides a necessary and sufficient condition for Markovianity of a quantum map. This is used to introduce a measure of non-Markovianity. This measure, however, requires demanding knowledge about the system and the environment. By using a quantum correlation monogamy property and an ancillary system, we propose a simplified measure with fewer requirements. Non-Markovianity is thereby decided by quantum state tomography of the system and the ancilla  

This study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of'robust stability testing function'and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order α belonging to [1,2), but only sufficient conditions for commensurate order α in interval (0,1). Besides, lower... 

A necessary and sufficient condition for the equivalence of two test functions is stated, also a necessary and sufficient condition for the existance of UMP test is proposed. Then it is shown, for the first time, that in coherent radar detection, UMP test does not exist and ALR and GLR detectors are not equivalent  

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... 

In this paper, a sufficient condition for existence of an overshoot in the step response of fractional-order systems is presented. Based on this condition, it can be shown that the existence of an overshoot in the step responses of some classes of fractional-order systems (for example, the class of fractional-order systems having commensurate orders between 1 and 2) is unavoidable. To show the usefulness of the obtained condition, this condition is applied to prove some results on the time response analysis of fractional-order control systems  

In this paper, the minimal state space realization of a fractional order transfer function is investigated in the sense of inner dimension both for commensurate and incommensurate cases. It is shown that while the traditional tools are applicable to check the minimality of a commensurate realization, there is no specific procedure to be certain about the minimality of incommensurate realizations. In this regard, the necessary and sufficient conditions are obtained for a specific class of fractional order transfer functions by which one can verify the existence of minimal realizations with inner dimension 2. Furthermore, a transformation is introduced through which all these realizations can... 

For a graph G, a zero-sum flow is an assignment of non-zero real numbers on the edges of G such that the total sum of all edges incident with any vertex of G is zero. A zero-sumk -flow for a graph G is a zero-sum flow with labels from the set {± 1, ..., ± (k - 1)}. In this paper for a graph G, a necessary and sufficient condition for the existence of zero-sum flow is given. We conjecture that if G is a graph with a zero-sum flow, then G has a zero-sum 6-flow. It is shown that the conjecture is true for 2-edge connected bipartite graphs, and every r-regular graph with r even, r > 2, or r = 3. © 2009 Elsevier Inc. All rights reserved  

In this paper, the synchronization of a pair of pacemaker cells as Sino-Atrial (SA) and Atrio-Ventricullar (AV) nodes have been studied and a new approach for synchronization, based on the concept of Phase Response Curve (PRC), has been proposed. The paper starts with presenting the necessary and sufficient conditions for synchronization in terms of the PRC parameters. Such conditions are time dependent and thus, the paper proceeds with deriving some sufficient conditions, which are not time dependent. The time-delay between the firing time of SA node and when it reaches the AV node is also considered. When the conditions for spontaneous synchronization are not valid, the synchronization is... 

The plausibility of embedding cycles of different lengths in the graphs of a network (known as the pancyclicity property) has important applications in interconnection networks, parallel processing systems, and the implementation of a number of either computational or graph problems such as those used for finding storage schemes of logical data structures, layout of circuits in VLSI, etc. In this paper, we present the sufficient condition of the pancyclicity property of OTIS networks. The OTIS network (also referred to as two-level swapped network) is composed of n clones of an n-node original network constituting its clusters. It has received much attention due to its many favorable... 

Decentralized integral controllability (DIC) is an important property of industrial and process multivariable control systems. In this paper, some of the previously proposed conditions for the study of the DIC of certain systems are extended to treat systems with correlated and independent uncertainty. These conditions are based on the concept of the stability of Polytopic and Interval family of matrices, and evaluation of the Lyapunov condition only at special vertices of these families. By comparison with previous sufficient conditions, and known necessary conditions, it is demonstrated that the newly proposed criteria are significantly less conservative, especially in the case of... 

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

We study the reliable transmission of correlated sources over the relay channel. One of the sources is available at the sender while the other one is known to the relay. The receiver wishes to reconstruct both sources. We find necessary and sufficient conditions for optimal separation of source and channel codes. The coding scheme is based on the combination of the Slepian-Wolf source coding and Partial Decode-and-Forward (PDF) strategy. In this scheme, the relay partially decodes the message transmitted by the sender. We also consider the semi-deterministic relay channel where the output at the relay is a deterministic function of inputs from the sender and the relay. For the transmission... 

The plausibility of embedding cycles of different lengths in the graphs of a network (known as the pancyclicity property) has important applications in interconnection networks, parallel processing systems, and the implementation of a number of either computational or graph problems such as those used for finding storage schemes of logical data structures, layout of circuits in VLSI, etc. In this paper, we present the sufficient condition of the pancyclicity property of OTIS networks. The OTIS network (also referred to as two-level swapped network) is composed of n clones of an n-node original network constituting its clusters. It has received much attention due to its many favorable... 

Decentralized controllers with integral action represent a large portion of multivariable controllers currently employed in the process industry. The integrity of these systems with respect to loop failures has been relatively well researched. In particular, important results have been found with respect to the relative gain array (RGA). However, less has been done on the treatment of the integrity of uncertain systems. This paper considers the integrity conditions of uncertain systems with norm-bounded uncertainties, and extends four existing integrity conditions to these uncertain systems. These are: integral stabilizable (IS), integral controllable (IC), integral controllable with... 

In this paper, we consider the reliable transmission of correlated sources over the relay channel. The destination wishes to find a lossless reconstruction of both sources. We find the sufficient conditions under which the relay can partially cooperate with the sender to transmit the sources to the destination. The achievability scheme is based on regular encoding/backward decoding strategy. The proposed region includes the known region for multiple-access channel with correlated sources and the achievable rate of relay channel with partial decode-and-forward strategy, as special cases. A class of deterministic relay channels is considered. It is shown that the error-free transmission of... 

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  

In an original impulsive synchronization only instantaneous errors are used to determine the impulsive inputs. To improve the synchronization performance, addition of an integral term of the errors is proposed here. In comparison with the original form, the proposed modification increases the impulse distances which leads to reduction in the control cost as the most important characteristic of the impulsive synchronization technique. It can also decrease the error magnitude in the presence of noise. Sufficient conditions are presented through four theorems for different situations (nominal, uncertain, noisy, and noisy uncertain cases) under which stability of the error dynamics is... 

This paper presents a new and ubiquitous framework for establishing achievability results in network information theory (NIT) problems. The framework is used to prove various new results. To express the main tool, consider a set of discrete memoryless correlated sources (DMCS). Assume that each source (except one, Z n) is randomly binned at a finite rate. We find sufficient conditions on these rates such that the bin indices are nearly mutually independent of each other and of Z n. This is used in conjunction with the Slepian-Wolf (S-W) result to set up the framework. We begin by illustrating this method via examples from channel coding and rate-distortion (or covering problems). Next, we... 

We present sufficient conditions for multicasting a set of correlated sources over cooperative networks. We propose a joint source-Wyner-Ziv encoding/sliding-window decoding scheme, in which each receiver considers an ordered partition of the other nodes. For each ordered partition, we obtain a set of feasibility constraints . We consolidate the results of the different ordered partitions by utilizing a result of geometrical approach to obtain the sufficient conditions. We observe that these sufficient conditions are indeed necessary conditions for Aref networks. As a consequence of the main result, we obtain an achievable rate region for networks with multicast demands. Also, we deduce an...