On the basis of the comparison method, sufficient conditions of polystability are derived for a class of nonlinear complex systems. The developed approach is applied for the stability analysis of ...mechanical systems composed of interacted subsystems with dissipative, gyroscopic and potential forces. Conditions of polystability of the trivial equilibrium positions of the considered systems are obtained. Two examples are given to demonstrate the effectiveness of the proposed results.
This paper is concerned with the problems of stability and stabilization for a class of nonlinear mechanical systems. It is assumed that considered systems are under the action of linear gyroscopic ...forces, nonlinear homogeneous positional forces and nonlinear homogeneous dissipative forces of positional–viscous friction. An approach to strict Lyapunov functions construction for such systems is proposed. With the aid of these functions, sufficient conditions of the asymptotic stability and estimates of the convergence rate of solutions are found. Moreover, systems with delay in the positional forces are studied, and new delay-independent stability conditions are derived. The obtained results are used for developing new approaches to the synthesis of stabilizing controls with delay in feedback law.
The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque ...tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or 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 analytical results.
For a certain class of nonlinear systems of differential equations with constant delay, we study the conditions for the asymptotic stability of the zero solution and the ultimate boundedness of the ...solutions. To obtain such conditions, we propose special constructions of Lyapunov–Krasovskii full-type functionals. Estimates of the transient time are found, and an analysis of the influence of perturbations on the dynamics of systems is carried out. In addition, we study the case in which the systems have switching operation modes and determine conditions under which the asymptotic stability or ultimate boundedness is preserved for any admissible switching laws.
The Russian Academy of Sciences and Federal Space Agency, together with the participation of many international organizations, worked toward the launch of the RadioAstron orbiting space observatory ...with its onboard 10-m reflector radio telescope from the Baikonur cosmodrome on July 18, 2011. Together with some of the largest ground-based radio telescopes and a set of stations for tracking, collecting, and reducing the data obtained, this space radio telescope forms a multi-antenna ground-space radio interferometer with extremely long baselines, making it possible for the first time to study various objects in the Universe with angular resolutions a million times better than is possible with the human eye. The project is targeted at systematic studies of compact radio-emitting sources and their dynamics. Objects to be studied include supermassive black holes, accretion disks, and relativistic jets in active galactic nuclei, stellar-mass black holes, neutron stars and hypothetical quark stars, regions of formation of stars and planetary systems in our and other galaxies, interplanetary and interstellar plasma, and the gravitational field of the Earth. The results of ground-based and inflight tests of the space radio telescope carried out in both autonomous and ground-space interferometric regimes are reported. The derived characteristics are in agreement with the main requirements of the project. The astrophysical science program has begun.
The role of the TAAR1 receptor, one of the trace amine-associated receptors (TAARs) family, in the formation of the behavioral component of the stress response was studied. The behavior of female ...TAAR1 knockout (TAAR1 KO) mice and wild-type (WT) mice was investigated in tests of elevated plus maze and elevated zero maze (EPM and EZM) and forced swimming test (FST) under normal conditions and after uncontrolled restraint stress exposure for 30 min. In the EPM test, the initial level of locomotor and exploratory activity, as well as the anxiety, was identical in both groups of mice. In the EZM test, the initial indicators of anxiety in female TAAR1 KO mice compared to female WT mice were higher, and locomotor activity was lower. When testing mice in the EZM 30 minutes after the end of stress exposure, it was found that the anxiety in female WT mice sharply increased, and the indicators of locomotor activity and exploratory behavior significantly decreased. The behavioral indicators in the EZM test in TAAR1 KO mice before and after stress were identical. A pronounced behavioral component of the stress response was observed in both TAAR1 KO and WT mice during testing in EPM. There were no significant differences between TAAR1 KO and WT mice during testing in EPM four hours after stress exposure. In the FST test the latency to the first immobility was initially longer in TAAR1 KO mice compared to the WT mice, but 24 hours after the stress this indicator has significantly decreased. As a result, TAAR1 KO and WT mice no longer differed in all behavioral indicators in the FST. Three weeks after acute restraint stress, both TAAR1 KO and WT groups showed a significant increase in immobility duration and a decrease in latency to the first immobility, however no difference between the both groups of animals were found. Thereby, we found the complete absence of behavioral change immediately after stressor exposure in TAAR1 KO compared to the WT mice.
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