The paper addresses the asymptotic stability problem for a class of difference systems with nonlinearities of a sector type and time-delay. A new approach to Lyapunov-Krasovskii functionals constructing for considered systems is proposed. On the basis of the approach, delay-independent asymptotic stability conditions and estimates of the convergence rate of solutions are derived. In addition, stability of perturbed systems is investigated in the case where nonstationary perturbations admit zero mean values. Some examples are given to illustrate the obtained results. (c) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The problem of monoaxial stabilization of a rigid body is studied. It is assumed that a linear time-invariant dissipative torque and a time-varying restoring torque vanishing as time increases act on the body. Both the case of linear restoring torque and that of essentially nonlinear one are considered. With the aid of the decomposition method, conditions are obtained under which we can guarantee the asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of our theoretical results.

The paper deals with a dynamically symmetric satellite in a circular near-Earth orbit. The satellite is equipped with an electrodynamic attitude control system based on Lorentz and magnetic torque properties. The programmed satellite attitude motion is such that the satellite slowly rotates around the axis of its dynamical symmetry. Unlike previous publications, we consider more complex and practically more important case where the axis is fixed in the orbital frame in an inclined position with respect to the local vertical axis. The satellite stabilization in the programmed attitude motion is studied. The gravitational disturbing torque acting on the satellite attitude dynamics is taken into account since it is the largest disturbing torque. The novelty of the proposed approach is based on the usage of electrodynamic attitude control system. With the aid of original construction of a Lyapunov function, new conditions under which electrodynamic control solves the problem are obtained. Sufficient conditions for asymptotic stability of the programmed motion are found in terms of inequalities for the values of control parameters. The results of a numerical simulation are presented to demonstrate the effectiveness of the proposed approach. (C) 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.

The topic of the article is an artificial Earth satellite in a circular near-Earth orbit. The satellite possesses a dynamical symmetry and is equipped with an electrodynamic attitude control system based on the usage of Lorentz and magnetic torques. The control torques are ensured by a controllable variation of two electromagnetic parameters of the satellite: the intrinsic magnetic moment and the static moment of charge of the first order. In the satellite's programmed motion the axis of the dynamical symmetry is inclined to the local vertical axis at a constant angle and the satellite slowly rotates around that axis. Such a rotation mode is of great importance in space missions, because it can reduce the temperature gradient effect, which may cause problems with the satellite's functioning. But this mode cannot be realized without a control because of the disturbances, among which the gravitational torque should be mentioned as the most important one. In the present paper the satellite's stabilization in the programmed attitude motion is investigated. The stated problem appears to be more complex than the problem of the uniaxial attitude stabilization of a satellite, and previously it was not treated with the use of the electrodynamic control system. On the basis of the Lyapunov direct method the conditions, under which the electrodynamic control solves the problem, were obtained. A new construction of the Lyapunov function was proposed, and using the function sufficient conditions for the asymptotic stability of the programmed motion were found in an explicit form.

We consider a hybrid dynamical system composed of a family of subsystems of nonlinear differential equations and a switching law which determines the order of their operation. It is assumed that subsystems are homogeneous with homogeneity degrees less than one, and zero solutions of all subsystems are asymptotically stable. Using the Lyapunov direct method and the method of differential inequalities, we determine classes of switching laws providing prescribed estimates of domains of attraction for zero solutions of the corresponding hybrid systems. The developed approaches are used for the stabilization of a double integrator.

Stability of certain classes of nonlinear time-delay switched systems is studied. For the corresponding families of subsystems, conditions of the existence of common Lyapunov–Razumikhin functions are found. The fulfilment of these conditions provides the asymptotic stability of the zero solutions of the considered hybrid systems for any switching law and for any nonnegative delay. Some examples are presented to demonstrate the effectiveness of the obtained results.

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated.In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

This paper examines certain classes of multiconnected (complex) systems with time-varying delay. Delay-independent stability conditions and estimates of the convergence rate of solutions to the origin for those systems are derived. It is shown that the exponents in the obtained estimates depend on the parameters of Lyapunov functions constructed for the corresponding isolated subsystems. The problem of computing parameter values that provide the most precise estimates is investigated. Some examples are presented to demonstrate the effectiveness of the proposed approaches.

Certain classes of essentially nonlinear nonstationary systems are studied. With the aid of the Lyapunov direct method and the averaging technique, conditions are obtained under which the zero solutions of the considered systems are stable with respect to all variables and asymptotically stable with respect to a part of variables. It is shown that the proposed approach can be used for the stability analysis of equilibrium positions of nonlinear mechanical systems. Some examples are presented to demonstrate the effectiveness of our results.

Stability of the trivial equilibrium position for a class of hybrid mechanical systems with nonswitched linear velocity forces and switched nonlinear nonhomogeneous positional forces is studied. Sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the existence of a common Lyapunov function for the family of subsystems corresponding to a switched system, and therefore to ensure that the equilibrium position of the switched system is asymptotically stable for an arbitrary switching signal. In the case when we are failed to prove the existence of a common Lyapunov function, classes of switching signals are determined for which one can guarantee the asymptotic stability. An example is presented to demonstrate the effectiveness of the proposed approaches.

We consider a nonlinear complex (large-scale) system with time delay. It is assumed that the corresponding isolated subsystems are homogeneous, and the zero solutions of the sub- systems are asymptotically stable when delay is equal to zero. By the Lyapunov direct method, and the Razumikhin approach, delay-independent stability conditions for the complex system are obtained. These conditions are formulated in terms of solvability of auxiliary systems of al- gebraic inequalities. An example is given to demonstrate effectiveness of the presented results.

Certain classes of systems with nonlinearities of a sector type and time-varying delay are studied. By the use of the Lyapunov functions method and the Razumikhin approach, conditions are obtained under which the zero solution of considered systems is asymptotically stable for an arbitrary continuous nonnegative and bounded delay. Moreover, estimates of the convergence rate of solutions are derived.

A switched system generated by the family of homogeneous subsystems with homogeneity orders less than one is studied. It is assumed that the zero solution of each subsystem is asymptotically stable. On the basis of the dwell-time approach, conditions on switching law are determined under which a given spherical neighborhood of the origin is contained in the attraction domain of the zero solution of the corresponding hybrid system.

The stability of the trivial equilibrium position of certain classes of mechanical systems with time-varying delay is studied. The considered systems are described by the second order differential equations in the Lagrange form. It is assumed that velocity forces are linear, whereas for positional forces both linear case and essentially nonlinear one are investigated. On the basis of the decomposition method, sufficient conditions of the asymptotic stability of the equilibrium position are found. It is shown that the proposed approach can be used for the stability analysis of hybrid mechanical systems with switched positional forces. Three examples are presented to demonstrate the effectiveness of the obtained results. Key–Words:Mechanical systems, asymptotic stability, Lyapunov function, delay, hybrid system

A class of nonlinear nonstationary systems of Persidskii type is studied. The right-hand sides of the systems are represented in the form of linear combinations of sector nonlinearities with time-varying coefficients. It is assumed that the coefficients possess mean values. By means of the Lyapunov direct method, it is proved that if the investigated systems are essentially nonlinear, i.e. the right-hand sides of the systems do not contain linear terms with respect to phase variables, then the asymptotic stability of the zero solutions of the corresponding averaged systems implies the local uniform asymptotic stability of the zero solutions for original nonstationary systems. We treat both cases of delay free and time delay systems. Furthermore, it is shown that the proposed approaches can be used as well for the stability analysis of some classes of nonlinear systems with nontrivial linear approximation.

This paper addresses the ultimate boundedness and permanence analysis for a Lotka-Volterra type system with switching of parameter values. Two new approaches for the constructing of common Lyapunov function for the family of subsystems corresponding to the switched system are suggested. Sufficient conditions in terms of linear inequalities are obtained to guarantee that the solutions of the considered system are ultimately bounded or permanent for an arbitrary switching signal. An example is presented to demonstrate the effectiveness of the proposed approaches.

The nanoscale information is essential to understand the performance limiting features. In this work an electrochemical atomic force microscopy (EC-AFM) method is used to provide the surface topology of a Nafion® membrane and provides a detailed picture of proton conductivity on the nm-scale, allowing comparison to existing X-ray scattering methods. The observed dynamics of large conductivity changes of Nafion® is reflected in the formation of current pathways at room temperature and given relative humidity. Time resolved experiments are used to compare with theories of proton conduction in fuel cell membranes and verify models of microphase-separated structure derived from existing microscopic data. Furthermore, the measured current values reveal a remarkable correlation with the size of the conductive areas. Analysis of the distribution of conductive areas on the Nafion® surface suggests that there are different mechanisms which contribute to the proton current in Nafion® membrane. Additionally, time dependence in local conductivity is found and analyzed in terms of redistribution of water in the membrane. A statistical analysis of the current distribution is performed and compared with theoretical simulations. Evidence is found for the existence of a critical current density. On a timescale of seconds the response of the conductive network is probed by applying voltage steps to the AFM tip. Die Polymer-Elektrolytmembran ist die Schlusselkomponente einer Brennstoffzelle. Das Hauptziel dieser Arbeit war mit Hilfe von elektrochemischer Rasterkraftmikroskopie eine auf nanometer-aufgeloste Darstellung der Protonenleitfahigkeit einer Nafion-Membranoberflache zu gewinnen. Der Schwerpunkt lag hierbei auf der Untersuchung der Zusammenhange zwischen Ionenleitfahigkeit und Nanostruktur einer Nafion Membran unter der definierten Luftfeuchtigkeit und angelegten Spannung. Auserdem wurde der zeitliche Verlauf des Stroms bei Anlegen von Potentialstufen ermittelt, um zu einem besseren Verstandnis der im Membraninnern stattfindenden Transportvorgange zu gelangen. Die vorgestellte Methode wurde hier entwickelt und erstmals eingesetzt. In den letzten zwei Jahren ist die Anzahl an Publikationen uber elektrochemische Rasterkraft Mikroskopie deutlich gestiegen, was das grose wissenschaftliche Interesse an diesen Systemen beweist. Es ist davon auszugehen, dass viele der Membranhersteller die neue Messmethode anwenden werden, da damit die Qualitat der Membran und der Zusammenhang mit den Details des Herstellungsprozesses besser verstanden werden konnen. Gleichzeitig bietet sie Einblick in die fundamentalen Prozesse der Protonenleitung und in ortliche und zeitliche Modulationen der Eigenschaften der verwendeten Polymere. Mit diesem Verstandnis kann zu einer Optimierung der Struktur der leitfahigen Membranen fur eine Steigerung der Brennstoffzellen Performance fuhren.