title: Investigation of ultimate boundedness conditions of mechanical systems via decomposition
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhan, Jingyuan
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-07-17T11:08:35Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-07-17T11:08:35Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov A. Yu., Zhan J. Investigation of ultimate boundedness conditions of mechanical systems via decomposition. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 2, pp. 173–186.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.202
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15951
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A mechanical system with linear velocity forces and nonlinear homogeneous positional ones is studied. It is required to obtain conditions for the ultimate boundedness of motions of this system. To solve the problem, the decomposition method is used. Instead of the original system of the second order equations, it is proposed to consider two auxiliary subsystems of the first order. It should be noted that one of these subsystems is linear, and another one is homogeneous. Using the Lyapunov direct method, it is proved that if the zero solutionsof the isolated subsystems are asymptotically stable, and the order of homogeneity of the positional forces is less than one, then the motions of the original system are uniformly ultimately bounded. Next, conditions are determined under which perturbations do not disturb the ultimate boundedness of motions. A theorem on uniform ultimate boundedness by nonlinear approximation is proved. In addition, it was shown thatfor some types of nonstationary perturbations with zero mean values the conditions of this theorem could be relaxed. A mechanical system with switched nonlinear positional forces is also investigated. For the corresponding family of systems, a common Lyapunov function is constructed. The existence of such a function ensures that the motions of the considered hybrid system are uniformly ultimately bounded for any admissible switching law. Examples are presented demonstrating the effectiveness of the developed approaches.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The reported study was supported by the Russian Foundation for Basic Research (grant N 19-01-00146-a), by the Saint Petersburg State University (project Id: 37569826), by the National Natural Science Foundation of China (grant N 61803007) and by the Rail Transit Joint Funds of Beijing Natural Science Foundation and Traffic Control Technology (grant N L171001).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 15; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: mechanical system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ultimate boundedness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: homogeneous function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: decomposition
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov direct method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Investigation of ultimate boundedness conditions of mechanical systems via decomposition
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 173-186.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15951/1/173-186.pdf
resources.format: Adobe PDF
resources.size: 298,48 kB