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The problems of interval estimation and stabilization are studied for a class of generalized Persidskii systems. For this class of models with nonlinearities satisfying the incremental passivity property, the nonnegativity conditions are proposed and a nonlinear interval observer is synthesized. A nonlinear feedback is designed that uses the interval estimates. The conditions of stability of estimation and regulation errors are formulated using linear matrix inequalities. The efficiency of the proposed interval observer and controller is demonstrated for a recurrent neural network and a mechanical system with cubic nonlinearity.

Hintergrund und Zielstellung: Die COVID-19-Pandemie führte zu erheblichen Veränderungen an Büroarbeitsplätzen. Bislang bestehen nur wenige Studien zu den Auswirkungen der pandemiebedingten Einführung von digitaler, remote Zusammenarbeit auf Führungskräfte. Das Ziel dieser Studie ist es, zu untersuchen, welche Veränderungen und welche Unterstützung Führungskräfte während der COVID-19-Pandemie erlebt haben. Methoden: In dieser qualitativen Interviewstudie wurden 16 Führungskräfte mittels halbstrukturierter, leitfadengestützter Telefoninterviews von Mai bis Juli 2021 zu ihren Erfahrungen während der COVID-19-Pandemie befragt. Die erhobenen Daten wurden transkribiert, anonymisiert und induktiv anhand der Qualitativen Inhaltsanalyse nach Mayring ausgewertet. Ergebnisse: Die Führungskräfte berichteten zum einen von arbeitsorganisatorischen Veränderungen ihrer individuellen Arbeitsbedingungen und erhöhten Führungsanforderungen. Zum anderen beschrieben sie sowohl negative als auch positive Veränderungen in der inhaltlichen Zusammenarbeit, wie z. B. Herausforderungen in der digitalen Kommunikation, der Einarbeitung neuer Teammitglieder, aber auch eine Verbesserung der sozialen Beziehungen im Team. Unterstützung erlebten die Führungskräfte durch z. B. flexible Arbeitsbedingungen, Bereitstellung struktureller Angebote, adäquate technische Ausstattung, Unterstützung durch die Unternehmensleitung oder Kolleg:innen. Diskussion: In Anbetracht der Relevanz von Führungskräften in Transformationsprozessen und den an sie gestellten hohen Arbeits- und Führungsanforderungen ist die Sicherstellung bedarfsorientierter Unterstützung von Seiten der Organisation von besonderer Bedeutung. Um den Herausforderungen in Krisenzeiten wie der COVID-19-Pandemie begegnen zu können, sollten Organisationen ihren Führungskräften verhaltens- und verhältnispräventive Maßnahmen anbieten.

For a retarded nonlinear system with a Lipschitz nonlinearity on bounded sets outside the origin, this article proposes necessary conditions for application of the Lyapunov–Razumikhin method. The presented conditions are illustrated on the classes of linear and nonlinear homogeneous systems.

This paper reports the real time monitoring of siderite deposition, on both Au- and Fe-coated surfaces, using the changes in frequency and dissipation of quartz crystal microbalance with dissipation (QCMD). In an iron chloride solution saturated with carbon dioxide, buffered with sodium bicarbonate to pH 6.8, roughly spherical particles of siderite formed within 15 min, which subsequently deposited on the QCMD crystal surface. Imaging of the surface showed a layer formed from particles ca. < 0.5 μm in diameter. Larger particles are clearly deposited on top of the lower layer; these larger particles are >1 μm in diameter. Monitoring of the frequency clearly differentiates the formation of the lower layer from the larger crystals deposited on top at later times. The elastic moduli calculated from QCMD data showed a progressive dissipation increase; the modeling of the solid–liquid interface using a flat approximation resulted in a poor estimation of elastic and storage moduli. Rather, the impedance modeled as a viscoelastic layer in contact with a semi-infinite liquid, where a random bumpy surface with a Gaussian correlator is used, is much more accurate in determining the elastic and storage moduli as losses from the uneven interface are considered. A further step considers that the film is in fact a composite consisting of hard spherical particles of siderite with water in the vacant spaces. This is treated by considering the individual contributions of the phases to the losses measured, thereby further improving the accuracy of the description of the film and the QCMD data. Collectively, this work presents a new framework for the use of QCMD, paired with traditional approaches, to enhance the understanding of crystal deposition and film formation as well as quantify the often evolving mechanical properties.

An easy synthesis of novel highly functionalized 5,6-dihydroindolo[2,1-a]isoquinolines was developed via a pseudo four-component domino reaction of 1-aroyl-3,4-dihydroisoquinolines, terminal α,β-ynones, and malononitrile. The selective formation of this biologically relevant heterocyclic core was achieved using a one-pot approach under microwave irradiation. The formation of the same skeleton through the reaction of 5,6-dihydropyrrolo[2,1-a]isoquinolines with malonic acid dinitrile supports the proposed mechanism, involving the intermediate product of the three-component reaction. Furthermore, the disproval of an alternative reaction pathway, which involved the dimerization of malononitrile followed by three-component transformation, was demonstrated. Introducing the malononitrile dimer as a CH acid resulted in the formation of a different pyrido[3′,4′:4,5]pyrrolo[2,1-a]isoquinoline core. Additionally, the synthesized 5,6-dihydroindolo[2,1-a]isoquinolines were examined for their photophysical properties, revealing their attractive luminescent characteristics.

This article considers the state estimation problem for a class of nonautonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuous- and discrete-time scenarios. The requirements are formulated using linear matrix equalities (LME) and inequalities (LMI). We present two possible applications of the result, a reduced-order observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuous- and discrete-time settings. With nonlinear regression being a sophisticated case, the parameter estimation problem for a particular output equation (when the fusion of linear and nonlinear sensors is weighted) is investigated. Two nonlinear examples demonstrating the efficiency of results are provided.

The JEL classification system is a standard way of assigning key topics to economic articles to make them more easily retrievable in the bulk of nowadays massive literature. Usually the JEL (Journal of Economic Literature) is picked by the author(s) bearing the risk of suboptimal assignment. Using the database of the Collaborative Research Center from Humboldt-Universität zu Berlin we employ a new adaptive clustering technique to identify interpretable JEL (sub)clusters. The proposed Adaptive Weights Clustering (AWC) is available on http://www.quantlet.de/and is based on the idea of locally weighting each point (document, abstract) in terms of cluster membership. Comparison with k-means or CLUTO reveals excellent performance of AWC.

In this article, an approach is proposed for the remote observation of a dynamical system through a data-rate constrained communication channel. The focus is put on discrete-time systems with a Lipschitz nonlinearity, driven by an external signal, and subject to bounded state perturbation and measurement error. The problem at hand is providing estimates of system's state at a remote location, which is connected via a channel, which can only sent limited numbers of bits per unit of time. A solution, named observation scheme, is proposed in the form of several interacting agents. This solution is designed such that the maximum observation error is upper bounded by a computable quantity dependent on system constants and selectable parameters. The scheme is designed in an event-triggered fashion, such that the actual communication rate is sometimes much lower than the theoretically evaluated maximum one, as it is demonstrated through simulations.

A simple fixed-time converging estimation algorithm is presented for a linear regression using the dynamic regressor extension and mixing method within a discrete-time setting, with a persistently excited regressor and bounded measurement noises. The solution is based on Kreisselmeier's filters, and it is computationally simpler than the existing analogs.

This article deals with the problem of time-varying parameter identification in dynamical regression models affected by disturbances. The disturbances comprise time-dependent external perturbations and nonlinear unmodeled dynamics. With this aim in mind, we propose a robust nonlinear adaptive observer. The algorithm ensures the asymptotic convergence of the parameter identification error to an acceptably small region around the origin in the presence of disturbances. The synthesis of the adaptive observer is given in terms of linear matrix inequalities, providing a constructive design method. An academic example and a low inertia power system illustrate the robustness and the applicability of the proposed adaptive observer for the time-varying parameter identification problem.

For input-affine nonlinear dynamical systems, an input-to-state stability analysis with respect to (weighted) average values of exogenous perturbations is proposed. The time-delay method is used to represent the system in a suitable form for investigation: A kind of neutral-type differential equation. The introduced approach allows the asymptotic gains with respect to zero-mean periodic signals to be evaluated for nonlinear systems (an analogue of Bode magnitude plot), as well as for integral input-to-state stable systems with periodic inputs. The results are illustrated on the class of homogeneous systems.

Here we critically evaluate the literature on immunotherapy failure in inflammatory bowel disease patients. In particular anti-drug antibody production, and subsequently loss of response as the primary cause of immunotherapy failure in IBD patients. The benefits of shifting from the “standard” empirical dose escalation approach to therapeutic drug monitoring with anti-TNFαtherapy is explored. The American Gastroenterology Association and British Society of Gastroenterology both currently recommend the use of reactive therapeutic drug monitoring to guide treatment, following loss of response in inflammatory bowel disease patients with active disease. However, further research is required to prove the efficacy of a proactive therapeutic drug monitoring approach alone in remitted IBD patients. A combination of personalised monitoring approach for anti-drug antibodies and therapeutic drug monitoring could provide beneficial treatment outcome for people with inflammatory bowel disease by predicting drug failure prior to clinical symptoms and allowing timely switching to an alternative drug.

We present new results for the analysis of global boundedness of state periodic systems. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a part of the state vector, and the case of systems, whose dynamics is periodic with respect to all state variables. To derive the results, the notion of strong Leonov functions is introduced. The main results are complemented by a number of relaxations based on the concept of weak Leonov functions.

Abstract: With the development of oil fields, the proportion of the highest-molecular-weight components, asphaltenes, increases in the composition of the extracted raw materials. The propensity of asphaltenes to aggregate causes a number of problems, which makes the task of oil deasphalting relevant. In this work, studies on separation of the asphaltene fraction from oil using PAN membranes are carried out. To decrease the pore size of membranes obtained by a phase inversion method, an additional component, acetone, is introduced into the casting solution. The permeability of the resulting membranes for water is 37.6 ± 1.7 L m−2h−1atm−1and for toluene, 25.3 ± 1.8 L m−2h−1atm−1, and the pore size is 4.6 ± 0.5 nm. When filtering solutions of oil diluted with toluene (1 g/L), the retention of the membranes for asphaltenes is 73 ± 4%, while it exceeds 95% when the oil content in the solution is over 10 g/L. The parameters of membrane fouling during filtration of solutions of oil in toluene are studied. It is noted that, upon moving from toluene to solutions of oil, the permeability of the membranes decreases tenfold. At the same time, the decrease in permeability is reversible, and when the solution of oil is replaced by a pure solvent, the membrane restores up to 99% of its initial permeability.

Abstract: In modern conditions of constant adverse effects on living organisms, such as environmental pollution or global climate change, the study of deeply conserved mechanisms that contribute to the adaptation of animals to such conditions is of particular relevance. The influence of stress suffered at early stages of development on the formation of fitness and the endocrine status of adults has been repeatedly shown in various species of mammals. However, similar studies on arthropods have not previously been carried out, and one of the key differences between the ontogeny of holometabolous insects from mammals is metamorphosis, including the formation of a pupa and the histolysis of tissues and organs with the subsequent formation of new structures from its products and imaginal discs, which are formed in early ontogenesis. As a result, an almost new organism, an imago, is formed. Are the metabolic changes that occurred in the insect’s body under the influence of unfavorable external influences before the imaginal moult preserved, or does metamorphosis “erase” them? To answer this question, the effect of heat stress experienced by the larvae of Drosophila melanogasteron such signs of adult fitness as longevity, response to acute heat stress, and resistance to it is studied. The study results show that early mortality is reduced due to larval stress in both D. melanogastermales and females,although no changes in the maximum lifespan are recorded. At the same time, early stress leads to a decrease in resistance to acute heat stress and a corresponding drop in alkaline-phosphatase activity in both sexes. Thus, we can conclude that heat stress experienced by D. melanogasterduring the larval stage is not “reset” by metamorphosis, and causes significant changes in the fitness of adult individuals.

The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Robustness of the obtained control law is studied.

In this article, the effect of a homogeneous parasitic dynamics on the stability of a homogeneous system, when homogeneity degrees are possibly different, is studied via input-to-state stability approach in the framework of singular perturbations. Thus, the possibilities to reduce the order of the interconnected system considering only the reduced-order dynamics and neglecting the parasitic ones are examined. Proposed analysis discovers three kinds of stability in the behavior of such an interconnection by assuming that both, reduced-order and unforced parasitic dynamics, are globally asymptotically stable. In the first case, global asymptotic stability of the interconnection can be concluded, when the homogeneity degrees of both systems coincide and the singular perturbation parameter is small enough. In the second case, only local stability of interconnection can be ensured, when the homogeneity degree of reduced-order dynamics is greater than the homogeneity degrees of the parasitic ones. Helpfully, the proposed approach allows us to estimate the domain of attraction for the system's trajectories as a function of the singular perturbation parameter. In the third case, only practical stability can be guaranteed, when the homogeneity degree of reduced-order dynamics is smaller than the homogeneity degrees of the parasitic ones. Additionally, the proposed approach provides an estimation of the asymptotic bound of the system's trajectories in terms of the singular perturbation parameter.

Herein, we report a highly regioselective one-pot synthesis of pyrazolo[3,4-b]pyridines via the reaction of 3-arylidene-1-pyrrolines with aminopyrazoles. The reaction proceeds through the sequential nucleophilic addition/electrophilic substitution/C–N bond cleavage and provides easy access to pyrazolo[3,4-b]pyridine derivatives featuring a primary amino group. Moreover, the reaction can be terminated at the electrophilic substitution stage, thus providing convenient entry to the hardly accessible pyrazolopyrrolopyridine scaffold.

Abstract: Membranes have been fabricated from polyacrylonitrile (PAN) doped with graphene oxide (GO) particles, PAN pyrolyzed by IR irradiation (IR-PAN-a), and nanodiamonds (ND). The pore structure of the resulting membranes has been studied. It has been shown that the addition of carbonaceous components slightly reduces the average pore size of the membranes from 17 to 12–15 nm, thereby leading to a decrease in the water permeability of membranes from 158 to 80.9–119.9 kg/(m2h atm). Doping with particulate additives led to surface hydrophilization: the contact angle of water decreased from 65° to 48°–55°, facilitating the flow of crude oil solutions in toluene by a factor of 2–3 compared to the PAN membrane. However, the addition of GO or IR-PAN-a promoted a significant increase in irreversible membrane fouling. On the other hand, the addition of nanodiamonds not only reduced the overall fouling of the membrane and increased the permeability of the feed mixture from 4.93 to 8.47 kg/(m2h atm), but also made it possible to recover more than 96% of the pure toluene flux. The rejection ratio of ND-doped membranes during the filtration of 10 g/L oil solutions in toluene was 85–89%.

Abstract: The permanent is a multilinear function that is a “symmetric” analog of the determinant. In the present paper, we consider several properties of the permanent of matrices of small orders.

At the core of the aluminum (Al) ion battery is the liquid electrolyte, which governs the underlying chemistry. Optimizing the rheological properties of the electrolyte is critical to advance the state of the art. In the present work, the chloroaluminate electrolyte is made by reacting AlCl3with a recently reported acetamidinium chloride (Acet-Cl) salt in an effort to make a more performant liquid electrolyte. Using AlCl3:Acet-Cl as a model electrolyte, we build on our previous work, which established a new method for extracting the ionic conductivity from fitting voltammetric data, and in this contribution, we validate the method across a range of measurement parameters in addition to highlighting the model electrolytes’ conductivity relative to current chloroaluminate liquids. Specifically, our method allows the extraction of both the ionic conductivity and voltammetric data from a single, simple, and routine measurement. To bring these results in the context of current methods, we compare our results to two independent standard conductivity measurement techniques. Several different measurement parameters (potential scan rate, potential excursion, temperature, and composition) are examined. We find that our novel method can resolve similar trends in conductivity to conventional methods, but typically, the values are a factor of two higher. The values from our method, on the other hand, agree closely with literature values reported elsewhere. Importantly, having now established the approach for our new method, we discuss the conductivity of AlCl3:Acet-Cl-based formulations. These electrolytes provide a significant improvement (5–10× higher) over electrolytes made from similar Lewis base salts (e.g., urea or acetamide). The Lewis base salt precursors have a low economic cost compared to state-of-the-art imidazolium-based salts and are non-toxic, which is advantageous for scale-up. Overall, this is a noteworthy step at designing cost-effective and performant liquid electrolytes for Al-ion battery applications.

Electrocution is a death caused by an application of electrical current to the human body. Our present understanding of electrocution—as the induction of ventricular fibrillation (VF)—followed a nearly century-long path of misunderstandings and speculation primarily focused on hypotheses of asphyxia as well as central nervous system trauma. It is hard for us today to appreciate the past mystery of an unexpected sudden death usually bereft of visible trauma. Even today, a false dogma exists that direct-current shocks can cause asystole instead of VF. A lightning discharge (up to 500 megavolts) is differentiated because it can cause substantial acute and chronic neural effects leading to other cardiac arrest rhythms. The human heart is exquisitely sensitive to alternating currents, and VF can be induced with currents of one-eighth that required for mere pacing. Because of these low currents, this effect obtains only in the TQ interval, and low-power electrocution does not involve the vulnerable period. If a current is strong enough to electrocute, generally it will do so in 1–2 seconds; longer shocks do not tend to be more dangerous. Regardless of concomitant drug dosing, the electrocution cardiac arrest rhythm is still VF, suggesting that electrocution is a stand-alone cause of death; the electrical current does not potentiate the effects of the drug. The experimental and clinical data supporting VF as the mechanism for electrocution are provided.

This article presents the typification of zeolite raw materials from the Khonguruu deposit (Sakha Republic (Yakutia), Russia), in order to determine the area of its practical application in preparing the field for industrial development. The types of raw materials are distinguished by the difference in cation composition: clinoptilolite-geylandite composition (Na-and Ca-differences of zeolite) and geylandite composition (Ca-difference of zeolite). A brief description of the material composition and physicochemical properties of zeolite rocks is given. The physical and mechanical properties of the zeolite of the deposit and the possibility of its use for the purpose of drinking water purification are investigated. The performed studies have shown that the natural zeolite of Na-and Ca-differences has good sorption properties and can be used as filter materials in water purification systems intended for household and drinking purposes.

AbstractAn overview of the MEPhIST-0 educational and research small-scale spherical tokamak project is presented including the vacuum vessel, magnetic field systems, and diagnostics. In contrast to other small machines, it is an advanced tokamak with D-shaped plasma equipped with an electron-cyclotron resonance pre-ionization system for plasma startup and an ion-cyclotron resonance system for plasma heating and wall conditioning. The design choices taken are discussed from the perspective of a primarily educational installation. The machine design is simplified while remaining relevant to larger devices. First plasma results obtained in 2021 are presented.

A high-order sliding-mode adaptive observer is proposed to solve the problem of an adaptive estimation, i.e., the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, which do not need to satisfy a relative degree condition equal to one. This approach is based on a high-order sliding-mode observer and a nonlinear parameter identification algorithm. The practical, global, and uniform asymptotic stability of the adaptive estimation error, despite the external disturbances, is guaranteed through the small-gain theorem. The convergence proofs are developed based on the Lyapunov and input-to-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

In this article, input-to-state stability and stabilization conditions in time-delay generalized Persidskii systems are studied. These conditions are formulated in terms of linear matrix inequalities, which may depend on delay values, and be local or global in state-space. Numerical examples of opinion dynamics and the Lotka–Volterra model illustrate the efficiency of the proposed results.

This paper is devoted to the construction of continuous and periodic controllers for ISS or iISS stabilization of a class of multistable state periodic systems. For this purpose, the concepts of practical ISS-, ISS- and iISS-control Leonov functions are introduced. Then, it is proven that the existence of these functions is a sufficient condition to ensure that the system under study is ISS- or iISS stabilizable, and explicit feedback control laws can be obtained by means of a mild adaptation of Sontag's universal formula. The proposed method is illustrated by the design of an excitation controller for a synchronous generator ensuring ISS of the closed-loop system.

A time-varying state feedback is presented that guarantees stability with hyperexponential rate of convergence of all trajectories to the origin for a double integrator system. It is shown that this convergence property is uniform with respect to matched bounded external disturbances. An implicit time-discretization scheme of the closed-loop system is given, which preserves all main properties of the continuous-time counterpart, and in addition has bounded errors with respect to the measurement noises. Based on this discretization, for sampled-and-hold implementation, a modified linear time-varying state feedback is proposed providing an accelerated rate of convergence to the continuous-time plant. The efficiency of the suggested control is illustrated through numeric experiments.

This work deals with the problem of finite-time homogeneous observer design for linear systems. Compared to other works, the stability conditions and parameters tuning are formulated using linear matrix inequalities being less conservative. The proposed results are based on the homogeneity property and Implicit Lyapunov Function method. The results are supported with simulation examples.

The main task of sensors in public transport is to collect information about the transportation of passengers. One of the features of passenger traffic in Russian settlements is the low level of their organization. This is due, among other things, to the lack of professional analysis of traffic flows when designing route networks. The relevance of the work lies in increasing the efficiency of detecting urban passenger traffic using modern methods and algorithms. The article analyzes the current state of passenger traffic in the settlement, describes the role of technical and programs for monitoring passenger traffic, classifies their types and areas of application.

This work aims to propose conditions for the existence of an observer for a particular class of nonlinear systems, presented as an interconnection of two Persidskii systems. First, we establish analytical expressions for steady-state solutions of an interconnected system. Next, a reduced-order observer for this system is designed, and the stability and boundedness of the error dynamics are proven. An academic example and an example considering Chua's circuits illustrate our results.

Sufficient conditions for almost global synchronization in acyclic networks of Kuramoto oscillators with heterogeneous coupling strengths and natural frequencies are presented. The result is established by employing the recently developed Leonov function framework for systems whose dynamics are periodic for all state variables. The synchronization property is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria. The implications of these conditions on the network topology, the oscillator's coupling strengths and natural frequencies are discussed. Finally, the results are illustrated via a numerical example.

Observation and identification are important issues for the practical use of compartmental models of epidemic dynamics. Usually, the state and parameters of the epidemic model are evaluated based on the number of infected individuals (the prevalence) or the newly infected cases (the incidence). Other estimation techniques, for example, based on the exploitation of the proportion of primo-infected individuals (easily retrievable data), are rarely considered. We are thus interested in a general question: may the measure of the number of primo-infected individuals and the prevalence improve simultaneous state and parameter estimation? In this paper, we design a nonlinear adaptive observer for a simple infection model with waning immunity and consequent reinfections to answer this question. The practical asymptotic stability of the estimation errors is then proved using the Lyapunov function method. Finally, the convergence of the observer is illustrated in simulations.

Abstract: An Al–Fe–Cr–Co–Ni high-entropy alloy (HEA) coating is deposited on a substrate made of 5083 alloy using the cold metal transfer (CMT) technology (wire-arc additive manufacturing (WAAM) in combination with welding surfacing). The HEA alloy has a nonequiatomic composition. The modern physical materials science methods are used to analyze the structure, phase and elemental compositions, defect substructure of the coating–substrate system. It is shown that he elemental and phase compositions, the defect substructure of the coating are dependent on the distance from the zone of contacting the coating and the substrate. The layer with a thickness to 200 µm adjacent to the contact zone contains includes a second phase at the HEA grain boundaries rich in chromium and iron atoms. The microdiffraction analysis shows that these inclusions are Al8Cr5. It is revealed that nanocrystalline phases Al2O3and MgAlO with sizes 10–20 nm and a subgrained structure (subgrain size 140–170 nm) form in the zone of mixing the coating and substrate. The structure of the I type is characterized by inhomogeneous distribution of chemical elements in HEA; there are regions of lammelar shape enriched in Cr atoms and the regions of spherical shape enriched Ni, Fe, and Co atoms. Nanosized (NiCo)3, Al4, and Al13Fe4particles are arranged along the subgrain boundaries of the system. The physical mechanisms of increasing the material hardness in the coating-substrate contact are discussed.

The conditions for stability of the zero solution are formulated for homogeneous dynamical systems of non-zero degree with distributed delays. It is assumed that if the disturbances are absent and the non-delayed state substitutes the delayed one, then the obtained nominal system is globally asymptotically stable. In such a case it is proven that in the disturbance-free scenario the zero solution is locally asymptotically stable for positive degree and practically globally asymptotically stable for negative degree. Using averaging tools, the influence of time-varying disturbances is investigated and the respective stability margins are derived. Finally, the obtained theoretical findings are illustrated by a mechanical example.