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characteristic-polynomials
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Graphs whose spectrum determined by non-constant coefficients
, Article Electronic Notes in Discrete Mathematics ; Vol. 45 , 2014 , pp. 29-34 ; ISSN: 15710653 ; Kiani, D ; Mirzakhah, M ; Sharif University of Technology
Abstract
Let G be a graph and M be a matrix associated with G whose characteristic polynomial is M(G,x)=∑i=0nαi(G)xn-i. We say that the spectrum of G is determined by non-constant coefficients (simply M-SDNC), if for any graph H with ai(H)=ai(G), 0≤i≤n-1, then Spec(G)=Spec(H) (if M is the adjacency matrix or the Laplacian matrix of G, then G is called an A-SDNC graph or L-SDNC graph). In this paper, we study some properties of graphs which are A-SDNC or L-SDNC. Among other results, we prove that the path of order at least five is L-SDNC and moreover stars of order at least five are both A-SDNC and L-SDNC. Furthermore, we construct infinitely many trees which are not A-SDNC graphs. More precisely, we...
Comparison of the existing methods in determination of the characteristic polynomial
, Article Wec 05: Fourth World Enformatika Conference, Istanbul, 24 June 2005 through 26 June 2005 ; Volume 6 , 2005 , Pages 130-133 ; 9759845857 (ISBN); 9789759845858 (ISBN) ; Haeri, M ; Sharif University of Technology
2005
Abstract
This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented. COPYRIGHT © ENFORMATIKA
A relation between the Laplacian and signless Laplacian eigenvalues of a graph
, Article Journal of Algebraic Combinatorics ; Volume 32, Issue 3 , 2010 , Pages 459-464 ; 09259899 (ISSN) ; Ghorbani, E ; Koolen, J. H ; Oboudi, M. R ; Sharif University of Technology
2010
Abstract
Let G be a graph of order n such that ∑n i=0(-1) iailambdan-i and ∑n i=0(-1) iailambdan-i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that a i ≥b i for i=0,1,⋯,n. As a consequence, we prove that for any α, 0<α≤1, if q 1,⋯,q n and μ 1,⋯,μ n are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q 1 alpha+⋯+qα n≥μ α 1+⋯+μα n
Periodic characteristic ratio (PCR) method: An alternative method to determine the characteristic polynomial
, Article Mathematics and Computers in Simulation ; Volume 80, Issue 9 , May , 2010 , Pages 1841-1853 ; 03784754 (ISSN) ; Haeri, M ; Sharif University of Technology
2010
Abstract
This paper proposes an alternative method to determine the characteristic polynomial based on closed loop desired transient response. To develop the method, we have found optimal characteristic rations in simple arrangement of these parameters via performance map method. Despite its simplicity, the resulted system exhibits better transient response in comparison with the systems obtained from existing methods of determining the characteristics polynomials. Numerical simulations are used to illustrate the specifications of the proposed method
Reducing conservatism in robust stability analysis of fractional-order-polytopic systems
, Article ISA Transactions ; Volume 119 , 2022 , Pages 106-117 ; 00190578 (ISSN) ; Dehghani, M ; Tavazoei, M. S ; Sharif University of Technology
ISA - Instrumentation, Systems, and Automation Society
2022
Abstract
This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore...
Robust D-stabilization analysis of fractional-order control systems with complex and linearly dependent coefficients
, Article IEEE Transactions on Systems, Man, and Cybernetics: Systems ; 2020 ; Fathi Jegarkandi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check...
Robust D-stabilization analysis of fractional-order control systems with complex and linearly dependent coefficients
, Article IEEE Transactions on Systems, Man, and Cybernetics: Systems ; Volume 52, Issue 3 , 2022 , Pages 1823-1837 ; 21682216 (ISSN) ; Fathi Jegarkandi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2022
Abstract
This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check...
CDM-based design and performance evaluation of a robust AQM method for dynamic TCP/AQM networks
, Article Computer Communications ; Volume 32, Issue 1 , 2009 , Pages 213-229 ; 01403664 (ISSN) ; Haeri, M ; Sharif University of Technology
2009
Abstract
A new robust AQM strategy for dynamically varying TCP/AQM networks is proposed and its performance is investigated through computer simulations in MATLAB and ns-2 environments. The developed AQM is designed based on coefficient diagram method (CDM), which is a new indirect pole placement method that considers the speed, stability and robustness of the closed loop system in terms of time domain specifications. Simulation results indicate that the new method (CDM-AQM) performs very well for network variations both in topology and traffic. Besides, a new adaptive controller based on CDM as an AQM method is introduced. In the developed adaptive AQM (ACDM), the output feedback pole placement is...