title: Poincare mapping for a time-delay impulsive observer
metadata.name: dc.contributor.author
metadata.value: Yamalova, Diana R.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-07-05T09:11:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-05T09:11:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Yamalova D.R. Poincare mapping for a time-delay impulsive observer. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 1, pp. 64–77.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6688
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This note deals with a hybrid static gain observer for a linear time-invariant continuous plant under
  an intrinsic pulse-modulated feedback. The pulse parameters representing the discrete state of the hybrid
  system are not available for direct measurement and has to be estimated through continuous measurements.
  It poses an unusual observation problem. A considerable number of papers is devoted to the observability
  of hybrid systems, where the discrete states of a system are usually assumed known, while observers for
  hybrid systems that are able to reconstruct discrete states from only continuous measurements are not
  so well covered in the literature. With the time delay taken into account, the pulse-modulated model
  acquires an infinite-dimensional continuous part. The closed-loop dynamics become therefore both hybrid
  and infinite-dimensional, and this combination is mathematically challenging and so far rarely treated.
  However, the cascade structure of the continuous part, together with the impulsive feedback, allow the
  application of the concept of finite-dimensional reducibility (FD-reducibility), in particular the fact, that
  the dynamics of an impulsive time-delay system with an FD-reducible continuous part coincide on certain
  time intervals with the dynamics of a delay-free impulsive system. This idea plays a key role in the
  present study. Nevertheless the observer proposed here explicitly involve a delay and based on the infinitedimensional
  original plant model, on the one hand it complicates the study of its properties, but on the
  other allows observation of the system for the entire time interval.
  An pointwise discrete mapping (known in the hybrid systems theory as Poincare mapping), describing
  the observer dynamics is derived, constituting the contribution of the paper. With the use of this pointwise
  mapping the mathematical modeling of the system can be performed and obtained the observer stability
  conditions for synchronous mode with respect to the periodic solution of the system. Refs 14. Figs 2.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке СПбГУ (грант №6.38.230.2015) и РФФИ (грант
  №14-01-00107-a).
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. Mathematics. Mechanics. Astronomy;Volume 4 (62); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: time-delay systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: impulsive systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: state observer
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Poincare mapping for a time-delay impulsive observer
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 09-Yamalova.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6688/1/09-Yamalova.pdf
resources.format: Adobe PDF
resources.size: 669 kB