Stability Conditions Research Articles

Crucial factors for decision-making in international real estate development projects: Evidence from Chinese developers

This study aims to investigate the crucial factors influencing decision-making in international real estate development projects. The identification of these factors was initially derived from a comprehensive literature review and further refined through expert input from Chinese real estate developers. Subsequently, questionnaires were administered to these experts in three focus groups. The key determinants for decision-making in international real estate development projects were identified as follows: political stability condition of the host country, international diplomatic relations between the host and home country, macro-economic situation of the host country, maturity of real estate market in the host country, project financing, and international experience of the enterprise. The most significant categories encompassed political, economic, and project factors. This study addresses the scarcity of literature on international real estate development, with a specific focus on developers originating from developing nations. It has the potential to enrich the discourse surrounding international real estate practices and contribute valuable insights for future academic investigations.

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

Про стійкість обертання вільної системи двох пружно зв’язаних гіроскопів Лагранжа, один з яких має ідеальну рідину

On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the fluid oscillation, a characteristic equation of the fifth order is obtained. On the basis of the Liénard – Chipart criterion written in the inor form, the necessary conditions for the stability of the uniform rotation of the Lagrange gyroscopes and the fluid are written out as a system of four inequalities. With respect to the elasticity coefficient, these inequalities have degrees 1, 3, 6 and 8, respectively. Analytical studies of the leading coefficients of these stability conditions are carried out. It is shown that when the center of mass of the first solid body with liquid or the second does not coincide with the common point of these bodies, then at sufficiently large values of the elasticity coefficient the necessary stability conditions will always be satisfied. In the absence of elasticity in the hinge, the characteristic equation has a double zero root and in this case the stability conditions require additional studies. The obtained stability conditions are exact for an ellipsoidal cavity and approximate for other axisymmetric cavities. To clarify the obtained glass conditions for these voids, it is necessary to take into account additional tones of oscillation of an ideal liquid.

Stability Conditions and Stiffness Variability of General Tensegrity Systems with Kinematic Joints

Abstract Tensegrity systems represent promising candidate mechanisms with in-situ stiffness variability through changing the cables' prestress levels. However, prestress-based stiffness behaviors of tensegrity systems with arbitrary kinematic joints have not been analyzed systematically. This paper adopts the natural absolute coordinates for static modeling of tensegrity systems consisting of rigid members and tension elements. Then, a generic stiffness analysis method is developed to formulate the reduced-basis tangent stiffness matrix, which is found to include three parts: positive semi-definite material and geometric stiffness matrices, and an indefinite constraint stiffness matrix. Based on these findings, a systematic stability-checking procedure is derived to determine prestress and super stability, which are qualitative indicators of the softening and stiffening effects in different tensegrity systems. Then, we proceed to quantify the range of prestress-based stiffness variability by formulating semidefinite programming problems that numerically pinpoint the maximum and zero stiffness points. Furthermore, this paper reveals the composable nature of multiple self-stress states, enabling the composability of stiffness properties in mechanism designs. Several numerical examples verify the efficacy and versatility of the proposed method and demonstrate interesting stiffness behaviors of tensegrity systems with kinematic joints.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

Mini-Worskhop: Artin Groups meet Triangulated Categories

Artin and Coxeter groups are naturally occurring generalisations of the braid and symmetric groups respectively. However, unlike for Coxeter groups, many basic group theoretic questions remain unanswered for general Artin groups – most notably the K(\pi,1) -conjecture for Artin groups remains open except for certain special families of Artin groups. Recently, Artin groups have also appeared as groups acting on triangulated categories, where the associated spaces of Bridgeland’s stability conditions provide new realisations of the corresponding K(\pi,1) spaces. The aim of the workshop is to bring together experts and early career researchers from two seemingly different areas of research: (i) geometric and combinatorial group theory and topology, and (ii) triangulated categories and stability conditions, to explore their intersection via the K(\pi,1) -conjecture.

Controllability and Optimal Fast Operation of Nonlinear Systems

A new method for solving the problem of controllability and optimal transient behavior of nonlinear systems subject to boundary conditions and constraints on control values was proposed. Unlike existing methods, this new approach is based on constructing a general solution of the integral equation for a linear controlled system, followed by transforming the original problem into a special initial optimal control problem. We propose a new method for studying the global asymptotic stability of dynamical systems with a cylindrical phase space with a countable equilibrium position based on a non-singular transformation of the equation of motion and estimation of improper integrals along the solution of the system. Conditions for global asymptotic stability were obtained without involving any periodic Lyapunov function, as well as the frequency theorem. The effectiveness of the proposed method is shown with an example.

Long-Term Survival of Enterococcus faecium under Varied Stabilization and Cell Immobilization Conditions

Long-Term Survival of Enterococcus faecium under Varied Stabilization and Cell Immobilization Conditions

Composite Sand–Clay Infrastructural Soil Fills: Characteristic Consolidation and Hydraulic Properties

In the design construction of infrastructural projects comprised of geotechnical applications, including composite soil fill layers, compacted sand-clay soil fills are widely preferred as barrier layers, particularly in solid waste landfills, to minimize leakage, to prevent leachate from entering into groundwater. When bentonite clay with high water absorption capacity and low hydraulic conductivity is mixed with sand possessing relatively enhanced frictional properties, greater shear strength capacity, an effective fill material exhibiting low sensitivity to frost, and low volume change in case of wetting, drying can be obtained. On the other hand, when montmorillonite clay is loaded, due to highly critical volumetric contraction or dilation characteristics (high compressibility nature of clay), the soil fill composed of sand-clay will significantly consolidate. This situation may cause differential settlement problems of infrastructural fills employed in geotechnical applications. In this regard, the load conditions (mechanical effects) and the environmental conditions (physicochemical effects) in the field control compressibility characteristics and consolidation properties of sand-bentonite clay mixtures. This will ultimately impact the desired stability conditions of sand-clay soil layers built for constructed infrastructural fill, resulting in a deviation from anticipated performance conditions. To this end, in this study, the specimens of sand-bentonite clay mixtures prepared with different contents of sand-bentonite clay were subjected to one-dimensional consolidation tests to investigate the effect of bentonite content used in the mixture on consolidation behavior, hydraulic properties, and effect of sand amount on rate of consolidation and on resulting compressive strength behavior.

On stability of nonlinear difference equations and some of their applications

The issues of stability in solving nonlinear difference equations were considered. Based on a generalized difference analog of the well-known Bihari lemma, stability conditions for a trivial solution based on initial data were obtained, and an a priori estimate of stability under permanent disturbances was determined. The results were used to study the stability of solving explicit and implicit difference schemes approximating nonlinear parabolic equations.

Extended state observer-based finite-time trajectory tracking control for wheeled mobile robots under FDI attacks

The trajectory tracking control of wheeled mobile robots (WMRs) under False Data Injection (FDI) attacks is investigated in this paper. First, to mitigate the impact of FDI attacks, a finite-time extended state observer (FTESO) is constructed. The error dynamic of the tracking control system is then split up into two subsystems via the cascaded control approach, and a one-to-one finite-time control law is designed for both subsystems. Second, a new stability condition is proposed to ensure that the tracking error system is finite-time globally uniform ultimate bounded (GUUB) and the tracking error can converge into a compact set. Finally, it is validated that the proposed control method is effective through simulation studies.

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions.

MIMO Super-Twisting Controller using a passivity-based design

A novel MIMO Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a time and state-varying but unknown left matrix factor. Sufficient conditions for stability with full-matrix control gains are established, in contrast to the usual scalar gains. For this a smooth Lyapunov function, based on a passivity interpretation, is used. Moreover, continuous and homogeneous approximations of the classical discontinuous Super-Twisting algorithm are obtained, using a unified analysis method. Moreover, the proposed Super-Twisting algorithm is of the discontinuous type, in contrast to the usual unitary type.

New charged anisotropic solution in f(Q)-gravity and effect of non-metricity and electric charge parameters on constraining maximum mass of self-gravitating objects

In the present article, A new class of singularity-free charged anisotropic stars is derived in f(Q)-gravity regime. To solve the field equations, we assume a particular form of anisotropy along with an electric field and obtain a new exact solution in f(Q)-gravity. The explicit mathematical expression for the model parameters is derived by the smooth joining of the obtained solutions with the exterior Reissner–Nordstrom de-Sitter solution across the bounding surface of a compact star along with the requirement that the radial pressure vanishes at the boundary. We have modeled four self-gravitating pulsar objects such as LMC X-4, PSR J1903+327, PSR J1614-2230, and GW190814 in our current study and predict the radii of these objects that fall between 8 and 10 km. Furthermore, the physical validity of the solution is performed for self-gravitating object PSR J1614-2230 with mass 1.97±0.04M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.97\\pm 0.04~M_{\\odot }$$\\end{document} with radius 10 km. The solution successfully fulfills all the physical requirements along with the stability and hydrostatic equilibrium conditions for a well-behaved model. The non-metricity f(Q)-parameter χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}$$\\end{document} and electric charge parameter η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} play an important role in the maximum mass of the objects. The maximum mass increases when χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}$$\\end{document} and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} increase but a non-collapsing stable object can be obtained when χ1≤0.0205\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}\\le 0.0205$$\\end{document} and η≤0.0006\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\le 0.0006$$\\end{document}.

Finite-time formation trajectory tracking control for unmanned underwater vehicles with time delays and Markov-switch topology

ABSTRACT The formation trajectory tracking control strategy of unmanned underwater vehicles is proposed for communication time delay and communication topology random switching. The methods ensure that formation systems are finite-time bounded under discrete time. Firstly, based on the consistency theory and the exact feedback linearised dynamics model of unmanned underwater vehicle, a control strategy is proposed for discrete formation system with communication time delay. Secondly, a cooperative control method is designed for communication problems of Markovian switching topology and time delay. Then, definition of finite-time bounded and linear matrix inequality technique are applied to sufficient conditions of system stability for the above problem. Finally, the formation motion of discrete unmanned underwater vehicle system in three-dimensional space is simulated, fully demonstrating the feasibility of the method.

On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative

In this paper, the uniform asymptotic practical stability of nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse is examined using an auxiliary Lyapunov functions which are analogues of vector Lyapunov functions. Together with comparison results, sufficient conditions for the uniform practical stability as well as the uniform asymptotic practical stability of the impulsive Caputo fractional order systems are established. An illustrative example is given to confirm the suitability of the obtained results.

Mixed material point method formulation, stabilization, and validation for a unified analysis of free-surface and seepage flow

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions.

Takagi–Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems

In this paper, a Takagi–Sugeno fuzzy parallel distributed compensation control (TS-PDCC) is proposed for low-frequency oscillation (LFO) suppression in wind energy-penetrated power systems. Firstly, the fuzzy C-mean algorithm (FCMA) is applied to cluster the daily average wind speed of the wind farm, and the obtained wind speed clustering center is used as the premise variable of TS-PDCC, which increases the freedom of parameter setting of the TS fuzzy model and is closer to the actual working environment. Secondly, based on the TS fuzzy model, the TS-PDCC is designed to adjust the active power output of the wind turbine for LFO suppression. To facilitate the computation of controller parameters, the stability conditions are transformed into a set of Linear Matrix Inequalities (LMIs) via the Schur complement. Subsequently, a Lyapunov function is designed to verify the stability of the wind energy-penetrated power system and obtain the parameter ranges. Simulation cases are conducted to verify the validity and superior performance of the proposed TS-PDCC under different operating conditions.

Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane

The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.

Interval State Estimation of Systems with Metzler Polytopic Models

The paper deals with the design of interval observers for interval-defined strictly Metzler polytopic positive systems. The stability conditions for the proposed structure of the interval observer are formulated using linear matrix inequalities to ensure a positive estimate of the system state. The proposed method makes it possible to calculate time-varying lower and upper estimates of the state vector, assuming that the disturbance is bounded. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.