Search results for: Lyapunov exponents

Authors: Olga I. Moskalenko, Vladislav A. Khanadeev, Anastasya D. Koloskova, Alexey A. Koronovskii, Anatoly A. Pivovarov

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Generalized synchronization is one of the most intricate phenomena in nonlinear science. It can be observed both in systems with a unidirectional and mutual type of coupling including the complex networks. Such a phenomenon has a number of practical applications, for example, for the secure information transmission through the communication channel with a high level of noise. Known methods for the secure information transmission needs in the increase of the privacy of data transmission that arises a question about the observation of such phenomenon in systems with a complex topology of chaotic attractor possessing two or more positive Lyapunov exponents. The present report is devoted to the study of such phenomenon in two unidirectionally and mutually coupled dynamical systems being in chaotic (with one positive Lyapunov exponent) and hyperchaotic (with two or more positive Lyapunov exponents) regimes, respectively. As the systems under study, we have used two mutually coupled modified Lorenz oscillators and two unidirectionally coupled time-delayed generators. We have shown that in both cases the generalized synchronization regime can be detected by means of the calculation of Lyapunov exponents and phase tube approach whereas due to the complex topology of attractor the nearest neighbor method is misleading. Moreover, the auxiliary system approaches being the standard method for the synchronous regime observation, for the mutual type of coupling results in incorrect results. To calculate the Lyapunov exponents in time-delayed systems we have proposed an approach based on the modification of Gram-Schmidt orthogonalization procedure in the context of the time-delayed system. We have studied in detail the mechanisms resulting in the generalized synchronization regime onset paying a great attention to the field where one positive Lyapunov exponent has already been become negative whereas the second one is a positive yet. We have found the intermittency here and studied its characteristics. To detect the laminar phase lengths the method based on a calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been verified using the example of two unidirectionally coupled Rössler systems being in the band chaos regime. We have revealed the main characteristics of intermittency, i.e. the distribution of the laminar phase lengths and dependence of the mean length of the laminar phases on the criticality parameter, for all systems studied in the report. This work has been supported by the Russian President's Council grant for the state support of young Russian scientists (project MK-531.2018.2).

Keywords: complex topology of attractor, generalized synchronization, hyperchaos, Lyapunov exponents

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Shreemoyee Sarkar, Vikhyat Chadha

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In this paper, the local fractal properties and chaotic properties of financial time series are investigated by calculating two exponents, the Local Hurst Exponent: LHE and Lyapunov Exponent in a moving time window of a financial series.y. For the purpose of this paper, the Dow Jones Industrial Average (DIJA) and S&P 500, two of the major indices of United States have been considered. The behaviour of the above-mentioned exponents prior to some major crashes (1998 and 2008 crashes in S&P 500 and 2002 and 2008 crashes in DIJA) is discussed. Also, the optimal length of the window for obtaining the best possible results is decided. Based on the outcomes of the above, an attempt is made to predict the crashes and accuracy of such an algorithm is decided.

Keywords: local hurst exponent, lyapunov exponent, market crash prediction, time series chaos, time series local fractal properties

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Authors: Aysegul Sener, Gonca Tuncel Memis, Mirac Kamislioglu

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Chaos theory is one of the new paradigms of science since the last century. After determining chaos in the weather systems by Edward Lorenz the popularity of the theory was increased. Chaos is observed in many natural systems and studies continue to defect chaos to other natural systems. Acid rain is one of the environmental problems that have negative effects on environment and acid rains values are monitored continuously. In this study, we aim that analyze the chaotic behavior of acid rains in Turkey with the chaotic defecting approaches. The data of pH degree of rain waters, concentration of sulfate and nitrate data of wet rain water samples in the rain collecting stations which are located in different regions of Turkey are provided by Turkish State Meteorology Service. Lyapunov exponents, reconstruction of the phase space, power spectrums are used in this study to determine and predict the chaotic behaviors of acid rains. As a result of the analysis it is found that acid rain time series have positive Lyapunov exponents and wide power spectrums and chaotic behavior is observed in the acid rain time series.

Keywords: acid rains, chaos, chaotic analysis, Lypapunov exponents

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Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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Authors: Ram Kishor

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The Lyapunov characteristic exponent (LCE) is an important tool to describe behavior of a dynamical system, which measures the average rate of divergence (or convergence) of a trajectory emanating in the vicinity of initial point. To analyze the behavior of nearby trajectory emanating in the neighborhood of an equilibrium point in the restricted three-body problem under the influence of perturbations in the form of radiation pressure and oblateness, we compute LCEs of first order with the help of slandered method which is based on variational equation of the system. It is observed that trajectories are chaotic in nature due positive LCEs. Also, we analyze the effect of radiation pressure and oblateness on the LCEs. Results are applicable to study the behavior of more generalized RTBP in the presence of perturbations such as PR drag, solar wind drag etc.

Keywords: Lyapunov characteristic exponent, RTBP, radiation pressure, oblateness

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Authors: Nelson Nenuwe

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The behavior of interacting electrons in one dimension was studied by calculating correlation functions and critical exponents at zero and external magnetic fields for arbitrary band filling. The technique employed in this study is based on the conformal field theory (CFT). The charge and spin degrees of freedom are separated, and described by two independent conformal theories. A detailed comparison of the t-J model with the repulsive Hubbard model was then undertaken with emphasis on their Tomonaga-Luttinger (TL) liquid properties. Near half-filling the exponents of the t-J model take the values of the strong-correlation limit of the Hubbard model, and in the low-density limit the exponents are those of a non-interacting system. The critical exponents obtained in this study belong to the repulsive TL liquid (conducting phase) and attractive TL liquid (superconducting phase). The theoretical results from this study find applications in one-dimensional organic conductors (TTF-TCNQ), organic superconductors (Bechgaard salts) and carbon nanotubes (SWCNTs, DWCNTs and MWCNTs). For instance, the critical exponent at from this study is consistent with the experimental result from optical and photoemission evidence of TL liquid in one-dimensional metallic Bechgaard salt- (TMTSF)2PF6.

Keywords: critical exponents, conformal field theory, Hubbard model, t-J model

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Authors: Raouf Fareh, Maarouf Saad, Sofiane Khadraoui, Tamer Rabie

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This paper presents a tracking control strategy based on Lyapunov approach for nonholonomic wheeled mobile robot. This control strategy consists of two levels. First, a kinematic controller is developed to adjust the right and left wheel velocities. Using this velocity control law, the stability of the tracking error is guaranteed using Lyapunov approach. This kinematic controller cannot be generated directly by the motors. To overcome this problem, the second level of the controllers, dynamic control, is designed. This dynamic control law is developed based on Lyapunov theory in order to track the desired trajectories of the mobile robot. The stability of the tracking error is proved using Lupunov and Barbalat approaches. Simulation results on a nonholonomic wheeled mobile robot are given to demonstrate the feasibility and effectiveness of the presented approach.

Keywords: mobile robot, trajectory tracking, Lyapunov, stability

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Authors: Adedayo Oke Adelakun

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The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential.

Keywords: hierarchical structure, periodically forced oscillator, noisy parameters, dynamical behaviour, F6 - duffing oscillator

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Authors: Rahele Mosleh

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This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.

Keywords: global stability, invariant solutions, Lyapunov function, stationary points

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Authors: Kotbi Lakhdar, Hachi Mostefa

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We show that a simple transformation between the regular lattices (the square, the triangular, and the honeycomb) belonging to the same dimensionality can explain in a natural way the universality of the critical exponents found in phase transitions and critical phenomena. It suffices that the Hamiltonian and the lattice present similar writing forms. In addition, it appears that if a property can be calculated for a given lattice then it can be extrapolated simply to any other lattice belonging to the same dimensionality. In this study, we have restricted ourselves on the spectral power amplification (SPA), we note that the SPA does not have an effect on the critical exponents but does have an effect by the criticality temperature of the lattice; the generalisation to other lattice could be shown according to the containment principle.

Keywords: ising model, phase transitions, critical temperature, critical exponent, spectral power amplification

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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Authors: Yi-Fei Yang, Nai-Bao He, Shao-Bang Xing

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This study investigates the permanent magnet synchronous linear motor (PMSLM) chaotic motion under the specific physical parameters, the stability and the security of motor-driven system will be unavoidably influenced. Therefore, it is really necessary to investigate the methods of controlling or suppressing chaos in PMSLM. Firstly, we derive a chaotic model of PMSLM in the closed-loop system. Secondly, in order to realize the local asymptotic stabilization of the mechanical subsystem and the global stabilization of the motor-driven system including electrical subsystem, we propose an improved uniting control lyapunov functions by introducing backstepping approach. Finally, an illustrated example is also given to show the electiveness of the obtained results.

Keywords: linear motor, lyapunov functions, chao control, hybrid controller

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: H. Ben Khlifa, W. Cheikhrouhou-Koubaa, A. Cheikhrouhou

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The orthorhombic Pr₀.₈Na₀.₂−ₓKₓMnO₃ (x = 0.10 and 0.15) manganites are prepared by using the solid-state reaction at high temperatures. The critical exponents (β, γ, δ) are investigated through various techniques such as modified Arrott plot, Kouvel-Fisher method, and critical isotherm analysis based on the data of the magnetic measurements recorded around the Curie temperature. The critical exponents are derived from the magnetization data using the Kouvel-Fisher method, are found to be β = 0.32(4) and γ = 1.29(2) at TC ~ 123 K for x = 0.10 and β = 0.31(1) and γ = 1.25(2) at TC ~ 133 K for x = 0.15. The critical exponent values obtained for both samples are comparable to the values predicted by the 3D-Ising model and have also been verified by the scaling equation of state. Such results demonstrate the existence of ferromagnetic short-range order in our materials. The magnetic entropy changes of polycrystalline samples with a second-order phase transition are investigated. A large magnetic entropy change deduced from isothermal magnetization curves, is observed in our samples with a peak centered on their respective Curie temperatures (TC). The field dependence of the magnetic entropy changes are analyzed, which shows power-law dependence ΔSmax ≈ a(μ0 H)n at the transition temperature. The values of n obey the Curie Weiss law above the transition temperature. It is shown that for the investigated materials, the magnetic entropy change follows a master curve behavior. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve for both samples.

Keywords: manganites, critical exponents, magnetization, magnetocaloric, master curve

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Authors: Kazem Ghanbari, Yousef Gholami

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This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators.

Keywords: fractional derivatives and integrals, Hamiltonian system, Lyapunov-type inequalities, stability, disconjugacy

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Authors: C. C. Egwuonwu, N. A. A. Okereke, K. O. Chilakpu, S. O. Ohanyere

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In this study, initial soil strength indices (qu) and stress-strain characteristics, namely failure strain (ϵf), area under the stress-strain curve up to failure (Is) and stress-strain modulus between no load and failure (Es) were investigated as potential indicators for characterizing the erosion resistance of two compacted soils, namely sandy clay loam (SCL) and clay loam (CL) in some selected sites in Enugu State, Nigeria. The unconfined compressive strength (used in obtaining strength indices) and stress-strain measurements were obtained as a function of moisture content in percentage (mc %) and dry density (γd). Test were conducted over a range of 8% to 30% moisture content and 1.0 g/cm3 to 2.0 g/cm3 dry density at applied loads of 20, 40, 80, 160 and 320 kPa. Based on the results, it was found out that initial soil strength alone was not a good indicator of erosion resistance. For instance, in the comparison of exponents of mc% and γd for jet index or erosion resistance index (Ji) and the strength measurements, qu and Es agree in signs for mc%, but are opposite in signs for γd. Therefore, there is an inconsistency in exponents making it difficult to develop a relationship between the strength parameters and Ji for this data set. In contrast, the exponents of mc% and γd for Ji and ϵf and Is are opposite in signs, there is potential for an inverse relationship. The measured stress-strain characteristics, however, appeared to have potential in providing useful information on erosion resistance. The models developed for the prediction of the extent or the susceptibility of soils to erosion and subjected to sensitivity test on some selected sites achieved over 90% efficiency in their functions.

Keywords: characterization of erodibility, selected sites in Enugu state, soil strength, stress-strain indices

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Mounir Bekaik, Messaoud Ramdani

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We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

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In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of this systems are obtained by solving a set of Linear Matrix Inequalities(LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: multi-agent, linear matrix inequalities (LMIs), kronecker product, sampled-data, Lyapunov method

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Mohammad Beyki, Justus Pawlak, Robert Patzke, Franz Renz

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In the context of planetary exploration, the MIMOS II (miniaturized Mössbauer spectrometer) serves as a proven and reliable measuring instrument. The transmission behaviour of the electronics in the Mössbauer spectroscopy is newly developed and optimized. For this purpose, the overall electronics is split into three parts. This elaboration deals exclusively with the first part of the signal chain for the evaluation of photons in experiments with gamma radiation. Parallel to the analysis of the electronics, a new method for the stability consideration of linear and non-linear systems is presented: The extended method of Lyapunov’s stability criteria. The design helps to weigh advantages and disadvantages against other simulated circuits in order to optimize the MIMOS II for the terestric and extraterestric measurment. Finally, after stability analysis, the controller design according to Ackermann is performed, achieving the best possible optimization of the output variable through a skillful pole assignment.

Keywords: Mössbauer spectroscopy, electronic signal amplifier, light processing technology, photocurrent, trans-impedance amplifier, extended Lyapunov method

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Authors: H. Tédjini, Y. Meslem, B. Guesbaoui, A. Safa

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Flexible AC Transmission Systems (FACTS) are potentially becoming more flexible and more economical local controllers in the power system; and because of the high MVA ratings, it would be expensive to provide independent, equal, regulated DC voltage sources to power the multilevel converters which are presently proposed for STATCOMs. DC voltage sources can be derived from the DC link capacitances which are charged by the rectified ac power. In this paper a new stronger control combined of nonlinear control based Lyapunov’s theorem and Ant Colony Algorithm (ACA) to maintain stability of multilevel STATCOM and the utility.

Keywords: Static Compensator (STATCOM), ant colony optimization (ACO), lyapunov control theory, Decoupled power control, neutral point clamped (NPC)

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Authors: S. Henine, A. Youkana

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This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established.

Keywords: asymptotic behavior, Gierer-Meinhardt systems, global existence, Lyapunov functional

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

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In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: Chang-Ho Lee, Seung-Hoon Lee, Myeong-Jin Park, Oh-Min Kwon

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This paper investigates improved stability criteria for sampled-data control of linear systems with disturbances and time-varying delays. Based on Lyapunov-Krasovskii stability theory, delay-dependent conditions sufficient to ensure H∞ stability for the system are derived in the form of linear matrix inequalities(LMI). The effectiveness of the proposed method will be shown in numerical examples.

Keywords: sampled-data control system, Lyapunov-Krasovskii functional, time delay-dependent, LMI, H∞ control

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