Stability Conditions Research Articles

Global Exponential Stability Conditions for Discrete-Time BAM Neural Networks Affected by Impulses and Time-Varying Delays

Global Exponential Stability Conditions for Discrete-Time BAM Neural Networks Affected by Impulses and Time-Varying Delays

Sampled-Data H∞ Dynamic Output-Feedback Control for NCSs With Successive Packet Losses and Stochastic Sampling.

The problem of sampled-data H∞ dynamic output-feedback control for networked control systems with successive packet losses (SPLs) and stochastic sampling is investigated in this article. The aim of using sampled-data control techniques is to alleviate network congestion. SPLs that occur in the sensor-to-controller (S-C) and controller-to-actuator (C-A) channels are modeled using a packet loss model. Additionally, it is assumed that stochastic sampling follows a Bernoulli distribution. A model is established to capture the stochastic characteristics of both the SPL model and stochastic sampling. This model is crucial as it allows us to determine the probability distribution of the sampling interval between successive update instants, which is essential for stability analysis. An exponential mean-square stability condition for the constructed equivalent discrete-time stochastic system, which also guarantees the prescribed H∞ performance, is established by incorporating probability theory. The desired controller is designed using a step-by-step synthesis approach, which may offer lower design conservatism compared to some existing methods. Finally, our designed approach using a networked F-404 engine system model is validated and its merits relative to existing results are discussed. The proposed method is finally validated by employing a networked model of the F-404 engine system. Furthermore, the advantages of our method are presented in comparison to previous results.

Stability condition for nilpotent singularities by its complex separatrices

This work is focused in the center problem for nilpotent singularities of differential systems in the plane. Although there are involved methods to approach the center problem in this work, we present a new stability criteria based on the existence of the complex separatrices passing through the singular point, and independent of the normal form. The algebraic method needs only the computation of such complex separatrices up to certain order, which can be done with a computer algebra package.

Harmonic metrics for the Hull–Strominger system and stability

We investigate stability conditions related to the existence of solutions of the Hull–Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull–Strominger system is recasted using non-Hermitian Yang–Mills connections and holomorphic Courant algebroids. Our main development is a notion of harmonic metric for the Hull–Strominger system, motivated by an infinite-dimensional hyperKähler moment map and related to a numerical stability condition, which we expect to exist for families of solutions. We illustrate our theory with an infinite number of continuous families of examples on the Iwasawa manifold.

TURKISH-GREEK RELATIONS: A FRAGILE STABILITY BETWEEN NEIGHBORS ON THE TWO SHORES OF THE AEGEAN SEA

This article considers the nature of Turkish-Greek relations, focusing on the question of how these should be characterized. This is animportant topic not only because there is a lack of a clear definition of the situation between the two countries in the literature, but also because providing a greater clarity of the issues about Turkish-Greek relations can assist in the long-term envisioning of a possible path that the two countries might take in the future. Employing a descriptive analysis, the article shows that a state of conflict rather than cooperation has determined the evolution of relations between Turkey and Greece. This sheds light on the intractable nature of the problems between the two countries, whether in Cyprus, the Aegean Sea, or the Eastern Mediterranean. The article concludes that Turkish-Greek relations are characterized by a historically grounded condition of fragile stability, with permanent tension and possible crisis prevailing, even if conflicts are frozen and war is not foreseen.

Experimental Evaluation of a Takagi–Sugeno Fuzzy Controller for an EV3 Ballbot System

In this paper, experimental results about the performance of a Takagi–Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration of the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. In this work, following the Takagi–Sugeno (TS) fuzzy control design methodology, the Parallel Distributed Compensation (PDC) approach is used in the design of the TSFC. The EV3BRS’s TS Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near the upright position of EV3BRS’s body. The Linear Matrix Inequality (LMI) approach was used to obtain the feedback gains for every local linear controller, guaranteeing, via a conservative stability condition, the global asymptotic stability of the overall fuzzy control system. The main goal of the control task consists of maintaining the EV3BRS’s body at its upright position. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry. The appropriate performance of the controller design is corroborated via experimentation.

Accurate and robust linear representation for containership stability conditions with ballast water

Stowage planning involves optimizing the placement of cargo on a ship while ensuring the ship's stability conditions are met. This optimization problem is typically formulated as a mixed-integer linear programming problem. However, a challenge arises in representing stability conditions as linear constraints since these conditions have non-linear relationships to the decision variables. Although there are methods for linearizing these stability conditions, they lack a systematic modeling approach and numerical verification of accuracy and reliability. In particular, the complex and diverse nature of ballast water contributes to significant non-linearity, posing a considerable challenge in developing an accurate linear approximation. This study proposes linear prediction methods that incorporate ballast water to address major stability conditions such as trim, drafts, shear force, bending moment, torsion, and transverse metacentric height. We introduce a comprehensive training and testing methodology for prediction, and validate the proposed method by comparing it with true values on two ships of different capacities, demonstrating its accuracy and scalability.

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.

Stability analysis of interval type-2 sampled-data polynomial fuzzy-model-based control system with a switching control scheme

AbstractThe stability of an interval type-2 (IT2) sampled-data (SD) polynomial fuzzy-model-based control system with a switching control scheme is studied in this paper. The uncertain nonlinear plant is depicted via an IT2 polynomial fuzzy model. To realize control, a switching IT2SD polynomial fuzzy controller is generated. This paper adopts a switching control scheme with a variable sampling period. The modeling domain consists of several sub-domains, and each sub-domain corresponds to a local IT2SD polynomial fuzzy controller. These local IT2SD polynomial fuzzy controllers form the switching IT2SD polynomial fuzzy controller. To aid in the stability analysis, this paper adopts a looped-functional-based technique. The imperfect premise matching concept is brought in to solve the mismatch dilemma caused by the SD control strategy and uncertainties. For decreasing the conservativeness, this paper takes into account the state information as well as the information of IT2 membership functions. The stability analysis is performed for each sub-domain, providing the potential for further relaxation. As polynomials exist in the stability conditions, this paper employs the sum-of-squares method for the stability investigation. The simulation outcomes confirm the efficacy of the proposed method.

Stability of the de-Sitter universe: one-loop nonlocal f (R) gravity

With the method of the background field expansion, we investigate the one-loop quantization of the Euclidean nonlocal f (R) model in the de-Sitter universe. We obtain the ghost-free condition (GFC) based on the transformation from the Jordan frame to the Einstein frame and the classical stability condition (CSC) satisfied \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{RR}^{\\left(0\\right)}-{\\phi }_{0}{F}_{RR}^{\\left(0\\right)}<0$$\\end{document}. We present the on-shell and off-shell one-loop effective action and quantum stability condition (QSC) by utilizing the generalized zeta-function. We find that under the fulfillment of GFC, CSC and QSC are inconsistent.

Effects of Urban Growth and Urbanization on the Social Environment: Case Study Old and Modern Cities of Yemen

Aim: This research was designed to study the effects of urban growth and urbanization on the social environment (Study of the state of growth and social changes in the old and modern cities of Yemen an example). Background: Yemenis have a rich history of urban centers, which have played a crucial role in trade, crafts, industries, and science. These cities have become distinct areas of cultural development, economic polarization, and cultural radiation. They are considered crucibles for social culturalintegration, nurseries for political growth, and areas for the development of national consciousness. The history of Yemen's cities and urban centers demonstrates the close link between trade, delivery routes, political governance centers, and city growth and development. Some Yemeni historical cities have played a vital role before Islam as political capitals, educators, and seaports. Cities have emerged as a result of the desire to coexist and achieve stability, reflecting spiritual, material, social, and political conditions. The growth of cities and architecture is a reflection of these changes. Methodology: The physical changes in the Republic of Yemen and the identification of the city of Aden were studied by reviewing the studies that monitored these changes and their social, economic and population effects. The study relied on secondary data in the first place. Conclusion: Yemen's population growth rate in 2004 was low at 3.01%, but it remains high due to economic and social developments and changes demographic factors such as fertility, mortality, and migration the growth rate was decreased at 2.20%. The 2004 General Population and Housing Census revealed that the resident population is spread across various governorates, with Ta'izz, Hodeidah, and Ibb having the highest proportions. The General Census of Population and Establishments revealed changes in the relative weight of the provincial population between the 1994 and 2004 censuses, with some governorates experiencing an increase in population relative to the population, while others experienced a decrease. The annual growth rate of the resident population was 3.0%, and the proportion of the young age group increased from 46.2% in 1994 to 51.5% in 2004. The gender ratio in Yemen is 104, with some governorates having a higher proportion of species due to urbanization (male than more than female), employment opportunities, or male labor migration. The Central Statistical Agency predicts that population growth will remain high over the next 20 years, with a natural increase rate of 3.01%. The proportion of married people in the population is higher for both sexes, possibly due to increased living costs and lack of adequate housing.

Analytical and numerical solutions to the Klein–Gordon model with cubic nonlinearity

In this paper, the nonlinear Klein–Gordon equation’s exact solutions are obtained through the application of an appropriate transformation based on He’s semi-inverse approach. This equation considered a generalization of other famous models in applied science, such as Phi-4 equation, Duffing equation, Fisher–Kolmogorov model through population dynamics and Hodgkin–Huxley equation that characterizes the propagation of electrical signals via nervous system. The suggested approach is simple, robust, and efficient, and its application in other partial differential equations in applied science seems promising. Numerical solution of the nonlinear Klein–Gordon equation is presented using finite difference method. The method’s accuracy is demonstrated by contrasting it with the exact solution that we obtained. The Von Neumann stability technique is applied to obtain the stability condition and a convergent test is presented Some 2D and 3D graphs matching to chosen solutions are simulated by taking into account appropriate values for the parameters.

Exact solitary wave propagations for the stochastic Burgers’ equation under the influence of white noise and its comparison with computational scheme

In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.

Backstepping Control Design in Conjunction with an EKF-based Sensorless Field-Oriented Control of an IPMSM

The collector and brushless electronic commutation machines have gained widespread utilization in industrial applications. Among these machines, internal permanent magnet synchronous motors (IPMSMs) have become increasingly popular due to their numerous advantages, including high torque/current and torque/inertia ratios, robust construction, high efficiency, and reliability. However, the incorporation of position sensors in IPMSMs has introduced challenges concerning their application, performance, mass production, and cost. Consequently, the implementation of sensorless control techniques has become essential in drive systems and various applications. This paper proposes a backstepping control approach for achieving speed sensorless control of IPMSMs, employing an extended Kalman filter (EKF). The first step involves developing a comprehensive nonlinear dynamical model of the IPMSM in the direct and quadrature (d-q) rotor frame and obtaining its corresponding state-space representation. Subsequently, backstepping controllers for rotor speed and current tracking are designed to ensure precise tracking and anti-disturbance performance. These controllers are integrated into the field-oriented control (FOC) scheme. The Lyapunov stability theorem is employed to guarantee the asymptotic stability condition of the backstepping controller. To address the challenge of estimating immeasurable mechanical parameters of the IPMSM and accurately tracking the system states, an EKF is designed. This filter enables the estimation of mechanical parameters and achieves high steady-state precision within a finite time. The effectiveness of the proposed methodology is demonstrated through simulations conducted under various dynamic operating conditions, including sudden torque load changes, command speed changes, and parameter variations.

Pressure Effects on the Structural, Electronic, Elastic, Optical, and Vibrational Properties of YMg Intermetallic Compounds:A First-Principles Study

Abstract The properties of YMg in B2 structure have been comprehensively analysed using the first-principles plane-wave pseudopotential method. Specifically, the structural, electronic, elastic, vibrational, and optical properties were investigated using the generalized gradient approximation (GGA) method in the context of density functional theory. The Vienna ab initio simulation package (VASP) was utilized for these calculations. The computed lattice parameter (3.803 Å) and bulk modulus (41.33 GPa) are consistent with the earlier data on ambient pressure. The electronic band structure and energy-dependent density of states reveal the metallic nature of the titled compounds. The Born stability requirements confirmed the mechanical stability. The analysis of Pugh's and Poisson's ratios and Cauchy's pressure reveals that YMg is ductile under the pressures in consideration. According to several anisotropy indices, the compound is noticeably anisotropic both in ambient and under pressure. Our investigation includes an analysis of several fundamental mechanical parameters of the material, including the bulk modulus, the pressure derivative of the Zener anisotropy factor, Poisson's ratio, isotropic shear modulus and Young's modulus with a particular focus on their dependence on pressure. We have determined that the elastic constants obtained remain mechanically stable, satisfying the Born Stability conditions even at high pressures of up to 60 GPa. To explore the dynamic stability of YMg, we analysed the material's phonon dispersion curves. The examined compound displays stability under dynamic conditions from 0 GPa to 30 GPa, as evidenced by its positive vibration frequencies. However, this stability is not sustained under higher pressure, as the compound becomes unstable after 30 GPa to 70 GPa. &amp;#xD;The electronic band structure and density of states diagrams demonstrate YMg's metallic properties. At atmospheric pressure (0 GPa), the total density of states (TDOS) near the Fermi level is approximately 1.63 states/eV, with pressure application reducing DOS. The dielectric function, refractive index, and energy loss spectra are examined within the 0–20 eV energy range. YMg exhibits its highest absorption between 4 and 11 eV. The peak optical conductivity is observed around 0.78 eV (equivalent to 1589.5409 nm), while the most significant energy loss occurs at 11.90 eV, roughly corresponding to 2.8 Hz in the ultraviolet spectrum. Moreover, we extensively analyzed the material's phonon thermodynamic and optical properties, providing insights into its behavior under various conditions. The outcomes acquired at zero pressure are generally coherent with the current theoretical values.

Analyses of the SIR Epidemic Model Including Treatment and Immigration

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete-time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points in the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of flip bifurcation. A feedback control strategy is applied to control the chaos occurring in the system after a certain period of time. We also perform numerical simulations to support analytical results. We do all these analyses for models with and without immigration and show the effect of immigration on dynamics.

The Collapse of the Vaults of the Ambato Matriz Church in the 1949 Earthquake: A Response with a Technical Approach

This research examines the structural behavior of the central vault of the Matriz church that collapsed during the 1949 earthquake in Ambato, Ecuador. Following the disaster, the church and Episcopal Palace were demolished. The central vault lacked buttresses and had large cracks two years before the collapse. A study was conducted using graphic restitution and the theory of limit analysis of structures to analyze the mechanical behavior of the central vault. The aim was to provide a technical explanation for the cause of the collapse beyond the impact of the earthquake. The limit analysis of structures is a tool that determines the technical stability conditions of a masonry structure using graphic statics. In this case, the respective checks of the structural behavior could be made, concluding that the structural ensemble of the central vault was unstable and could have collapsed at any moment, not necessarily due to an earthquake. The article is based on the research project “Architectural analysis of the central nucleus of Ambato between 1895 and 1949: styles, types, techniques, losses, and continuities”, which was conducted at the Universidad Técnica de Ambato, Ecuador, from 2021 to 2023.

Vacuum stability in the one-loop approximation of a 331 model

In this study, we analyze the vacuum stability of the economical 331 model at the one-loop level using the renormalization group equations and a single-scale renormalization method. By integrating these equations, we determine stability conditions up to the Planck scale, incorporating constraints from recent experimental data on new Higgs-like bosons, charged scalars, and charged and neutral gauge bosons. Our analysis uncovers intriguing relations between the mass of the heaviest scalar and the masses of exotic quarks, in order to ensure stability of the model up to the Planck scale. For the 331 energy scale used in this work, 18 TeV, we find an upper bound on the heaviest quark mass of the model, which is not so distant from future LHC runs, serving as bounds to be searched. Additionally, we explore relations between the scalar couplings coming stability and perturbativity conditions. These impose unprecedented constraints on the economical 331 model.

Unveiling Agricultural Shifts through Stakeholder Interactions and Strategic Dynamics in Green Rice Production

This study explores the strategic interactions among the government, growers, and the public within the context of green rice production, employing an evolutionary game theory framework. Recognizing the intricate dynamics of agricultural sustainability, we construct a three-party evolutionary game model to investigate the strategic decision-making processes and stability conditions of each stakeholder. The model assesses how various strategies evolve under the influence of economic incentives, regulatory measures, and public engagement. Through analytical and numerical methods, including stability analysis and MATLAB 2020b simulations, we identify the Evolutionarily Stable Strategies (ESS) that signify sustainable practices in green rice production. The results reveal that as government incentives for green production increase and fines for non-green practices are enforced, the likelihood of growers adopting sustainable practices significantly rises. Furthermore, the strategic enhancement of economic incentives and reputational factors not only bolsters governmental regulatory commitment but also reduces the necessity for public supervision, demonstrating a systemic shift towards self-regulation and market-driven sustainability. The simulations demonstrate the system’s evolution towards a stable state where governmental regulation is fully enforced, growers adopt green production universally, and public supervision becomes redundant. The findings underscore the importance of designing policy interventions that harmonize economic and environmental objectives, suggesting that well-structured incentives and regulatory measures can catalyze the transition towards sustainable agricultural practices. Additionally, our study highlights the pivotal role of establishing effective incentive structures that ensure the economic benefits of green production outweigh the costs, facilitating an autonomous regulatory system. This study contributes to the understanding of how strategic interactions shaped by policy and market forces can foster agricultural sustainability.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.