Search results for: Linear Eigenvalue Analysis

Authors: Attila Vámosi, Tamás Mankovits, Dávid Huri, Imre Kocsis, Tamás Szabó

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Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. For example rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. The shape optimization problem of rubber parts led to the study of FEM based calculation processes. This type of problems was posed and investigated by several authors. In this paper the time demand of certain calculation methods are studied and the possibilities of time reduction is presented.

Keywords: Rubber bumper, data acquisition, finite element analysis, support vector regression.

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

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This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.

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Authors: E. Ansari-Piri, N. Eghbali

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Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: Edward Aris D. Fajardo, Hamdi Muhyuddin D. Barra

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This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

Keywords: Double Delta Potential, Eigenstates, Eigenvalue, Numerov Method, Single Delta Potential

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Authors: Kreangkri Ratchagit

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This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

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This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: A. Meftah, D. Zarga, M. Yahiaoui

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In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.

Keywords: FGM plates, Navier method, vibratory behavior.

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Authors: Reza Nadimi, Fariborz Jolai

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This article combines two techniques: data envelopment analysis (DEA) and Factor analysis (FA) to data reduction in decision making units (DMU). Data envelopment analysis (DEA), a popular linear programming technique is useful to rate comparatively operational efficiency of decision making units (DMU) based on their deterministic (not necessarily stochastic) input–output data and factor analysis techniques, have been proposed as data reduction and classification technique, which can be applied in data envelopment analysis (DEA) technique for reduction input – output data. Numerical results reveal that the new approach shows a good consistency in ranking with DEA.

Keywords: Effectiveness, Decision Making, Data EnvelopmentAnalysis, Factor Analysis

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Authors: Reeta Devi, Hitender Kumar Tyagi, Dinesh Kumar

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In present scenario, cardiovascular problems are growing challenge for researchers and physiologists. As heart disease have no geographic, gender or socioeconomic specific reasons; detecting cardiac irregularities at early stage followed by quick and correct treatment is very important. Electrocardiogram is the finest tool for continuous monitoring of heart activity. Heart rate variability (HRV) is used to measure naturally occurring oscillations between consecutive cardiac cycles. Analysis of this variability is carried out using time domain, frequency domain and non-linear parameters. This paper presents HRV analysis of the online dataset for normal sinus rhythm (taken as healthy subject) and sudden cardiac death (SCD subject) using all three methods computing values for parameters like standard deviation of node to node intervals (SDNN), square root of mean of the sequences of difference between adjacent RR intervals (RMSSD), mean of R to R intervals (mean RR) in time domain, very low-frequency (VLF), low-frequency (LF), high frequency (HF) and ratio of low to high frequency (LF/HF ratio) in frequency domain and Poincare plot for non linear analysis. To differentiate HRV of healthy subject from subject died with SCD, k –nearest neighbor (k-NN) classifier has been used because of its high accuracy. Results show highly reduced values for all stated parameters for SCD subjects as compared to healthy ones. As the dataset used for SCD patients is recording of their ECG signal one hour prior to their death, it is therefore, verified with an accuracy of 95% that proposed algorithm can identify mortality risk of a patient one hour before its death. The identification of a patient’s mortality risk at such an early stage may prevent him/her meeting sudden death if in-time and right treatment is given by the doctor.

Keywords: Early stage prediction, heart rate variability, linear and non linear analysis, sudden cardiac death.

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Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

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There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

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In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: Asymptotic relative efficiency, non-linear rank-based, robust, rank estimates, variogram.

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Authors: Anas M. Fares, A. Touqan

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A common approach in resisting lateral forces is the use of reinforced concrete shear walls in buildings. These walls represent the main elements to resist the lateral forces due to their large strength and stiffness. However, such walls may contain many openings due to functional requirements, and this may largely affect the overall lateral stiffness of them. It is thus of prime importance to quantify the effect of openings on the dynamic performance of the shear walls. SAP2000 structural analysis program is used as a main source after verifying the results. This study is made by using linear elastic analysis. The results are compared to ASCE7-16 code empirical equations for estimating the fundamental period of shear wall structures. Finally, statistical regression is used to fit an equation for estimating the increase in the fundamental period of shear-walled regular structures due to windows openings in the walls.

Keywords: Concrete, earthquake-resistant design, finite element, fundamental period, lateral stiffness, linear analysis, modal analysis, rayleigh, SAP2000, shear wall, ASCE7-16.

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Authors: S. H. Nasseri, M. Sohrabi, E. Ardil

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In this paper, we give a certain decomposition of the coefficient matrix of the fully fuzzy linear system (FFLS) to obtain a simple algorithm for solving these systems. The new algorithm can solve FFLS in a smaller computing process. We will illustrate our method by solving some examples.

Keywords: Fully fuzzy linear system, Fuzzy number, LUdecomposition.

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Authors: Kulin Dave, Kapil Mohan

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Earthquakes are considered to be the most destructive rapid-onset disasters human beings are exposed to. The amount of loss it brings in is sufficient to take careful considerations for designing of structures and facilities. Seismic Hazard Analysis is one such tool which can be used for earthquake resistant design. Ground Response Analysis is one of the most crucial and decisive steps for seismic hazard analysis. Rapar district of Kutch, Gujarat falls in Zone 5 of earthquake zone map of India and thus has high seismicity because of which it is selected for analysis. In total 8 bore-log data were studied at different locations in and around Rapar district. Different soil engineering properties were analyzed and relevant empirical correlations were used to calculate maximum shear modulus (Gmax) and shear wave velocity (Vs) for the soil layers. The soil was modeled using Pressure-Dependent Modified Kodner Zelasko (MKZ) model and the reference curve used for fitting was Seed and Idriss (1970) for sand and Darendeli (2001) for clay. Both Equivalent linear (EL), as well as Non-linear (NL) ground response analysis, has been carried out with Masing Hysteretic Re/Unloading formulation for comparison. Commercially available DEEPSOIL v. 7.0 software is used for this analysis. In this study an attempt is made to quantify ground response regarding generated acceleration time-history at top of the soil column, Response spectra calculation at 5 % damping and Fourier amplitude spectrum calculation. Moreover, the variation of Peak Ground Acceleration (PGA), Maximum Displacement, Maximum Strain (in %), Maximum Stress Ratio, Mobilized Shear Stress with depth is also calculated. From the study, PGA values estimated in rocky strata are nearly same as bedrock motion and marginal amplification is observed in sandy silt and silty clays by both analyses. The NL analysis gives conservative results of maximum displacement as compared to EL analysis. Maximum strain predicted by both studies is very close to each other. And overall NL analysis is more efficient and realistic because it follows the actual hyperbolic stress-strain relationship, considers stiffness degradation and mobilizes stresses generated due to pore water pressure.

Keywords: DEEPSOIL v 7.0, Ground Response Analysis, Pressure-Dependent Modified KodnerZelasko (MKZ) model, Response Spectra, Shear wave velocity.

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

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Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: Ishapathik Das

Abstract:

The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: Model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs.

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Authors: Behnam Shirkhanghah, Vahid Shahbaznejhad-Fard, Houshyar Eimani-Kalesar, Babak Pahlevan

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Flat double-layer grid is from category of space structures that are formed from two flat layers connected together with diagonal members. Increased stiffness and better seismic resistance in relation to other space structures are advantages of flat double layer space structures. The objective of this study is assessment and calculation of Behavior factor of flat double layer space structures. With regarding that these structures are used widely but Behavior factor used to design these structures against seismic force is not determined and exact, the necessity of study is obvious. This study is theoretical. In this study we used structures with span length of 16m and 20 m. All connections are pivotal. ANSYS software is used to non-linear analysis of structures.

Keywords: Behavior factor, Double-layer, Intensified resistance, Non-linear analysis

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Authors: W. R. Li, J. K. Xia, R. Q. Peng, Z. Y. Guo, L. Jiang

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According to 3D magnetic circuit of the transverse flux PM linear machine, distribution law is presented, and analytical expression of axial end flux leakage is derived using numerical method. Maxwell stress tensor is used to solve detent force of mover. A 3D finite element model of the transverse flux PM machine is built to analyze the flux distribution and detent force. Experimental results of the prototype verified the validity of axial end flux leakage and detent force theoretical derivation, the research on axial end flux leakage and detent force provides a valuable reference to other types of linear machine.

Keywords: Transverse flux PM linear machine, flux distribution, axial end flux leakage, detent force.

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Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li

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In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords: Fractional order systems, Time delay, Characteristic equation.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

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In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: Guangbin Wang, Fuping Tan

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In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: Non-linear vibrations, Annular plates, Large amplitudes, FGM.

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Authors: C. Ardil

Abstract:

This paper introduces a new method for multiplecriteria decision making (MCDM) that avoids order reversal and ensures consistency in decision-making. The proposed method involves range targeting of benefit and cost criteria vectors for range normalization of the initial decision matrix. The Reference Linear Combination (RLC) is used to avoid the rank reversal problem. The preference order generated from the target score matrix does not require relative comparisons between alternatives but relies on a chosen reference solution point after transforming the original decision matrix into an MCDM problem by specifying the minimum and maximum bounds of each criterion. The efficiency and applicability of the proposed RLC method were demonstrated in the selection of commercial passenger aircraft. 

Keywords: Aircraft selection, reference linear combination (RLC), multiple criteria decision-making, MCDM

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

Abstract:

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: S.K.Ayyaswamy, S.Balachandran, K.Kannan

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Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

Keywords: Second stage spectral radius, Irreducible matrix, Derived graph

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Benedek Kovacs, Janos Toth

Abstract:

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

Keywords: Neural networks, parameter estimation, linear regression, kinetic models, reaction rate coefficients.

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Authors: Adam Czornik, Aleksander Nawrat

Abstract:

This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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Authors: S. H. Sabzpoushan

Abstract:

In this research we show that the dynamics of an action potential in a cell can be modeled with a linear combination of the dynamics of the gating state variables. It is shown that the modeling error is negligible. Our findings can be used for simplifying cell models and reduction of computational burden i.e. it is useful for simulating action potential propagation in large scale computations like tissue modeling. We have verified our finding with the use of several cell models.

Keywords: Linear model, Action potential, gating dynamics.

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