Stability Criterion Research Articles

Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems

In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T-S) fuzzy model described by fractional-order differential equations. A T-S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the n−m reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results.

Hierarchical Stability Conditions for Two Types of Time-Varying Delay Generalized Neural Networks.

In this article, the stability analysis for generalized neural networks (GNNs) with a time-varying delay is investigated. About the delay, the differential has only an upper boundary or cannot be obtained. For the both two types of delayed GNNs, up to now, the second-order integral inequalities have been the highest-order integral inequalities utilized to derive the stability conditions. To establish the stability conditions on the basis of the high-order integral inequalities, two challenging issues are required to be resolved. One is the formulation of the Lyapunov-Krasovskii functional (LKF), the other is the high-degree polynomial negative conditions (NCs). By transforming the integrals in N-order generalized free-matrix-based integral inequalities (GFIIs) into the multiple integrals, the hierarchical LKFs are constructed by adopting these multiple integrals. Then, the novel modified matrix polynomial NCs are presented for the 2N-1 degree delay polynomials in the LKF differentials. Thus, the hierarchical linear matrix inequalities (LMIs) are set up and the nonlinear problems caused by the GFIIs are solved at the same time. Eventually, the superiority of the provided hierarchical stability criteria is demonstrated by several numeric examples.

Stability Criteria in Plant Structures

Stability Criteria in Plant Structures

Existence theory for ψ -Caputo fractional differential equations

UDC 517.9 The target of this paper is to handle a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsuling a collective fractional derivative known as the ψ -Caputo fractional operator. The applied fractional operator generated by the kernel is of the following kind: k ( t , s ) = ψ ( t ) - ψ ( s ) . The existence of the solutions of the above-mentioned equations is tackled by using Mönch's fixed-point theorem combined with the technique of measures of noncompactness. In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system. Finally, an example is given to illustrate the viability of the reported results.

Magneto-Thermoelastic Principal Parameter Resonance of a Functionally Graded Cylindrical Shell with Axial Tension

The principal parameter resonance of a ferromagnetic functionally graded (FG) cylindrical shell under the action of axial time-varying tension in magnetic and temperature fields is investigated. The temperature dependence of physical parameters for functionally graded materials (FGMs) is considered. Meanwhile, the tension bending coupling effect is eliminated by introducing the physical neutral surface. The kinetic and strain energies are gained with the Kirchhoff–Love shell theory. Based on the nonlinear magnetization characteristics of ferromagnetic materials, the electromagnetic force acting on the shell is calculated. The nonlinear vibration equations are obtained through Hamilton’s principle. Afterward, the vibration equations are discretized and solved by Galerkin and multiscale methods, respectively. The stability criterion for steady-state motion is established utilizing Lyapunov stability theory. After example analysis, the effects of magnetic field intensity, temperature and power law index on the static deflection are elucidated. Subsequently, the impacts of these parameters, as well as axial tension, on the amplitude-frequency characteristics, resonance amplitude, and multiple solution regions are discussed explicitly. Results indicate that the stiffness can be enhanced due to the generation of static deflection. The amplitude decreases with increasing magnetic field intensity, temperature, and power law index. When the magnetic field intensity surpasses a threshold, the resonance phenomenon disappears.

Research on stability for blended-wing-body aircraft

The primary goal of this research is to research the stability properties of a blended-wing-body (BWB) aircraft. This section examines the assessment and selection of aircraft design parameters, planform design, and reflex wing and conducts a complete aircraft stability analysis. A BWB aircraft conceptual design has been completed and the design. To attain static stability, it was examined and refined. The BWB aircraft's study was performed at three distinct values. The analytical findings were used to calculate the angle-of-attack (AOA) and the stall AOA. We determined the estimated initial departure angle of attack and departure region by assessing the results of the trials and a set of stability criteria.

The Dynamics Stability Judging Method for a Gantry-type Welding Robot

In order to improve the dynamic performance of gantry-type welding robot, this paper introduces the structural dynamics model and Lyapunov stability criterion of the gantry-type welding robot frame with nine degrees of freedom. The dynamic equations of the welding robot satisfy the Euler–Lagrange form, and the calculation index of welding robot Lyapunov stability is judged by matrix eigenvalues. Combining with the specific design parameters of an industrial welding robot, the motion stability of the gantry-type welding robot frame and the displacement response of the welding torch are analyzed. The influence of the change of the frame design structure on the stability of the welding torch for end effector of welding robot is discussed, furthermore, the improvement direction of vibration damping and anti-interference of welding robot system is pointed out. Finally, the dynamics simulation of the optimized gantry-type welding robot end effector is carried out by using ADAMS software, and the torque variation curve of the end effector is obtained, which provides a strong basis for the selection of motor models and the design of control system.

Orbital stability of solitary wave solutions of a Hamiltonian PDE arising in magma dynamics

We consider a Hamiltonian PDE arising from a class of equations appearing in the study of magma dynamics in the Earth’s interior. Previously, it has been shown that the Hamiltonian PDE admits solitary wave solutions. Simpson et al. proved that the solitary wave solutions are orbitally stable for the case n=2. We verify the stability criterion analytically for the case n=3. Our results answer partially an open question proposed by Simpson et al. (2008).

Assessment of the stability of permafrost landscapes in the developed territories of Western Yakutia

Using GIS technologies, a Map of the resistance of permafrost landscapes of the developed territories of Western Yakutia on a scale of 1:1,000,000 to anthropogenic impacts was compiled. The ice content of the underlying rocks, soil temperature, the thickness of the active layer and the distribution of cryogenic processes were accepted as stability criteria. At the same time, a point system for assessing the stability of landscapes was used. Spatial analysis of permafrost landscapes showed that the largest areas are occupied by stable landscapes (66.8%), relatively stable and relatively unstable landscapes occupy 19,5 and 13,7%, respectively.

Further finite-time stability analysis of neural networks with proportional delay

Different from fixed delays between neurons, proportional delay is a time-varying unbounded delay. In this paper, the issue of finite-time stability of fractional-order neural networks with proportional delay is investigated. To address the proportional delay terms in the system, a new Gronwall-type inequality with delay is proposed. Based on this inequality, order-related criterion for finite-time stability of fractional-order neural networks with proportional delay is obtained. Finally, some numerical experiments demonstrate the effectiveness and superiority of the results.

Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method

In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.

Complementary extended state observer‐based model‐free sliding mode control for a PMSM in cathode copper production

AbstractThis study introduces a model‐free sliding mode control scheme based on a complementary extended state observer (CESO) for a permanent magnet synchronous motor (PMSM) in cathode copper production. First, an ultra‐local model of the PMSM is proposed. Compared with the existing ultra‐local model, the ultra‐local model proposed in this study divides the disturbances into periodic and aperiodic perturbations. Furthermore, based on the proposed ultra‐local model, a CESO is proposed. Compared to the linear extended state observer (LESO) and the non‐linear extended state observer (NLESO), the proposed CESO combines the advantages of the LESO and the NLESO. The proposed CESO exhibits reduced disturbance estimation errors and greater resilience to significant periodic and minor aperiodic disturbances. By leveraging the ultra‐local model, a novel combined control strategy is devised, utilizing the CESO and a model‐free sliding mode control. The stability of the proposed control scheme has been verified through the Lyapunov stability theorem and the Hurwitz stability criterion. Subsequently, comparative simulations on disturbance rejection are conducted under periodic and aperiodic disturbances, illustrating the efficacy of the proposed control approach.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

Mathematical Modelling of the Impacts of Morning Fatigue on Academic Performance: A Case Study of Federal University Wukari, Taraba State

Several authors have researched the phenomenon of sleep deprivation among students. In their studies, we discovered that they did not consider morning fatigue. So, we decided to fill the gap in the literature by using mathematical models to study the impact of morning fatigue. The aim is to develop mathematical modelling for the impact of morning fatigues on the academic performances of the students, a case study of the Federal University Wukari in Taraba State. In this project work, we formulated a mathematical model based on a system of ordinary differential equations to study the impact of morning fatigue on academic performance. We tested the model for existence and uniqueness and discovered that the model exists and that it is unique. The basic reproduction number was computed using the next-generation matrix approach. Questionnaires were distributed to 400 students and the data for this research were collected from the responses of the students. The result of the basic reproduction number shows that morning fatigue can be controlled. Using the Routh-Hurwitz criterion for local stability, the fatigue-free equilibrium (FFE) states of the model were established and proved to be locally asymptotically stable. Sensitivity analysis was then carried out to determine which parameters should be targeted by control intervention strategies of which the result shows that an increase in the acceptance of the control measure rate leads to a reduction in the prevalence of fatigue. Finally, a numerical simulation of the model was carried out and the result shows that Morning fatigue has a great impact on the academic performance of students. This means that there is a need for students to avoid reading till daybreak which in turn brings morning fatigue.

Robust non-monotonic Lyapunov based stability and stabilization methods for continuous-time systems: Applied on bilateral teleoperation system

This study introduces a Non-monotonic Lyapunov (NML) framework aimed at stability evaluation and controller design for continuous-time systems, particularly under conditions of uncertainty. Conventional Lyapunov techniques often exhibit a conservative nature, particularly in the context of uncertain systems, which necessitates the development of less conservative alternatives like NML. The NML methodology distinguishes itself by not imposing strict monotonicity requirements for demonstrating the decrease of a Lyapunov functional. Consequently, this paper derives new stability and stabilization criteria framed as matrix inequalities applicable to a specific class of uncertain systems. The practical applicability of the introduced approach is illustrated through controller design for uncertain systems, exemplified by a nonlinear bilateral teleoperation model. Assorted demonstrative examples and simulation outcomes support the findings, underscoring the NML approach’s efficaciousness.

Hydrostatic Pressure‐Tuning of Opto‐Electronic and Thermoelectric Properties Half‐Heusler Alloy RhTiP With DFT Analysis

ABSTRACTUtilizing DFT along with Boltzmann transport theory, the structural, elastic, electrical, optical, and thermoelectric properties of half‐Heusler compound RhTiP have been calculated in principle to examine the pressure effect in the range of 0–40 GPa. As pressure increases, the volume and normalized lattice parameter decreased. In addition to satisfying the Born stability criterion, which ensured the compound RhTiP “natural stability,” the zero pressure elastic constants and the pressure‐dependent elastic constants are positive up to 40 GPa. The band structure computations guarantee the semiconductor nature of RhTiP, as demonstrated by the presence of electronic band gap of 1.035 eV at zero pressure. Using the Voigt‐Reuss‐Hill (VRH) averaging scheme under pressure, we have determined the values of this compound's bulk modulus , shear modulus , Young's modulus , Pugh ratio , Poisson's ratio , and anisotropy factor . Because the bulk modulus responds linearly to pressure, the material's hardness increases as pressure rises. Additionally, under pressures up to 40 GPa, the optical characteristics of RhTiP, including their reflectivity, absorptivity, conductivity, dielectric constant, refractive index, and loss function, were assessed and discussed. Furthermore, the thermoelectric properties are also studied for the materials and supports the tunning of pressure. This study provides a gateway to how the optoelectronic and transport properties of cubic RhTiP could be tuned by employing external pressure.

Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.

The immune response formed by the introduction of a DNA vector containing a cDNA fragment of the human thyroid-stimulating hormone receptor gene into transgenic mice

The number of patients with autoimmune thyroid diseases (Graves’disease, Hashimoto’sthyroiditis) is increasing globally. The most important part in the diagnosis of Graves’ disease (GD) is the detection of autoantibodies to the thyrotropin receptor (TSHR) in Graves’ patients’ sera. For the differential diagnosis of antibodies to thyroid antigens, it is promising to use tests based on monoclonal antibodies to TSHR, which can be obtained not only as a result of immunization with native or recombinant TSHR protein, but also through DNA immunization with genetically engineered constructs containing fragments of the TSHR gene. Based on mRNA we isolated from the thyroid tissue in GD, a number of fragments of the thyrotropin receptor gene were cloned, suitable for DNA immunization of animals. The purpose of this work is to evaluate the immunogenic properties of one of the constructed vectors, pVAX1-TSHR (1160), in a mouse model. The successful inclusion of the extracellular domain gene fragment of the human TSHR (1160), which was transfected into CHO cells as a part of the pVAX1 vector was confirmed by immunoblotting and ELISA. The immune response formed to the injection of the pVAX1 vector into BALB/c mice, containing a fragment of the human TSHR gene, was detected in different versions of ELISA. Immunization of animals with the DNA vector pVAX1-TSHR according to an experimentally selected scheme was effective for the formation of mouse splenocytes, secreting antibodies to TSHR, which were used for successful hybridization. This was confirmed by the results of determining antibody production to TSHR in murine blood sera. The level of antibody production remained high (titer more than 1:10.000) at the 8th week of the experiment. As a result of selection of individual clones according to the criteria of proliferative activity and stability of antibody production, the most stable cultures secreting mAbs against TSHR were selected.

Finite-time contractive stability for fractional-order nonlinear systems with delayed impulses: Applications to neural networks

This paper deals with finite-time stability (FTS) and finite-time contractive stability (FTCS) criteria of fractional-order nonlinear systems (FONSs), where the state of the systems consists of a finite number of delayed impulsive instants. To achieve these results, we have extended the theories on FTS and FTCS criteria from integer-order NSs to fractional-order systems. Employing the fractional-order Lyapunov stability theory, the sufficient conditions of the above-mentioned stability criteria are derived for a class of FONSs with state-dependent delayed impulses. Then, to ensure the applicability of the proposed results, we have analyzed the desired performances for several neural network (NN) models, such as non-autonomous NNs (NANNs), Cohen–Grossberg NNs (CGNNs), switched NNs (SNNs) and bidirectional associative memory NNs (BAMNNs). Finally, four representative numerical examples are illustrated to demonstrate the assurance of the obtained stability conditions of the respective state-dependent impulsive fractional-order NNs (FONNs).