Analysis of the practical stability and sensitivity of linear dynamical systems with change of phase space measurability

Authors

  • Fedir G. Garashenko The complex systems modelling department of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine., Ukraine
  • Olga L. Soproniyk The Department of Mathematical Problems of Control and Cybernetics at Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine., Ukraine

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2016.3.08

Keywords:

practical stability, sensitivity of dynamical systems, systems with change of space measurability

Abstract

In this work, the models of linear parametric systems of ordinary differential equations with variable measurability of phase space are investigated. The theorems about the practical stability of linear parametrical systems with variable measurability are proved. It is important that the reverse theorem about practical stability of indicated systems is obtained. The algorithms and criteria of analysis of practical stability of linear parametrical systems with variable measurability of phase space at the presence of constantly occurring perturbations are shown. The matrix equations of sensitivity of linear parametrical systems with variable measurability of the phase space are researched. It was investigated that on the basis of methods of practical stability and conditions which satisfied sensitivity matrices it was possible to effectively find the estimations of parameters for an analysis of the system sensitivity with variable measurability of the phase space. Results of given investigations can be successfully applied in the tasks of digital data processing and pattern recognition.

Author Biographies

Fedir G. Garashenko, The complex systems modelling department of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

Garashchenko Fedir,

professor, Doctor of Engineering Science, Chairman at the complex systems modelling department of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

Scope of research – qualitative analysis and evaluation of program trajectories in control systems; development of problems of practical stability of dynamic systems and the development of numerical methods to determine the optimal estimates; development of methods of structural and parametric undifferentiated trajectory optimization; solving problems of sensitivity and calculation of tolerances for parameters.

Olga L. Soproniyk, The Department of Mathematical Problems of Control and Cybernetics at Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine.

Olga Soproniuk,

the assistant at the Department of Mathematical Problems of Control and Cybernetics at Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine.

Scientific research – Practical stability and sensitivity in Systems with the Phase Space Variable Measurability.

References

Sopronjuk F.O. Modeljuvannja ta optymizatsija system upravlinnja z rozhaluzhennjam struktur / F.O. Sopronjuk. — Chernivtsi: Ruta, 1995. — 155 s.

Kirichenko N.F. Vvedenie v teoriju stabilizatsii dvizhenija / N.F. Kyrychenko. — K.: Vyshcha shk., 1978. — 184 s.

Bublik B.N. Strukturno-parametricheskaja optimizatsija i ustojchivost' dinamiki puchkov / B.N. Bublik, F.G. Garaschenko, N.F. Kirichenko. — K.: Nauk. dumka, 1985. — 304 s.

Harashchenko F.H. Analiz ta otsinka parametrychnykh system / F.H. Harashchenko, L.A. Pantaliyenko. — K.: IDDO, 1995. — 140 s.

Harashchenko F.H. Prykladni zadachi teoriyi stijkosti / F.H. Harashchenko, V.V. Pichkur. — K.: VPTs "Kyyivs'kyj universytet", 2014. — 125 s.

Garaschenko F.G. Adaptivnye modeli approksimatsii signalov v strukturno-parametricheskih klassah funktsij / F.G. Garaschenko, O.S. Degtjar, O.F. Shvets' // Problemy upravlenija i informatiki. — 2011. — № 2. — S. 69–77.

Harashchenko F.H. Vstup do analizu chutlyvosti parametrychnykh system: navch. posib. / F.H. Harashchenko, O.F. Shvets'. — K.: VPTs "Kyyivs'kyj universytet", 2006. — 115 s.

Garaschenko F.G. Analiz i otsenka parametricheskih sistem na osnove metodov prakticheskoj ustojchivosti / F.G. Garaschenko, L.A. Pantalienko // Problemy upravlenija i informatiki. — 1996. — № 1, 2. — S. 145–161.

Rozenvasser E.N. Chuvstvitel'nost' sistem upravlenija / E.N. Rozenvasser, R.M. Jusupov. — M.: Nauka, 1981. — 464 s.

Garaschenko F.G. Issledovanie zadach teorii chuvstvitel'nosti metodami prakticheskoj ustojchivosti / F.G. Garaschenko, L.A. Pantalienko // Izv. AN SSSR. — Tehnicheskaja kibernetika. — 1989. — Vyp. 6. — S. 17–25.

Shvets' O.F. Modeli dlja analizu chutlyvosti rozryvnykh dynamichnykh system zi zminnoju vymirnistju fazovoho prostoru / Shch.F. Shvets', O.L. Sopronjuk // Visn. Kyyiv. nats. un-tu imeni Tarasa Shevchenka. Serija: Fizyko-matematychni nauky. — 2009. — № 1. — S. 158–162.

Sopronjuk O.L. Pro matrychni modeli dlja chyslovoho analizu parametrychnoyi chutlyvosti system zi zminoju vymirnosti fazovoho prostoru / O.F. Shvets', O.L. Sopronjuk // Visn. Kyyiv. nats. un-tu imeni Tarasa Shevchenka. Serija: Fizyko-matematychni nauky. — 2010. — № 1. — S. 132–136.

Garaschenko F.G. Issledovanie zadach rascheta dopuskov na parametry s pomosch'ju metodov prakticheskoj ustojchivosti / F.G. Garaschenko, L.A. Pantalienko // Avtomatika i telemehanika. — 1993. — № 4. — S. 43–55.

Sopronjuk O.L. Optymal'ne otsinjuvannja dopuskiv na parametry u dynamichnykh systemakh zi zminoju vymirnosti fazovoho prostoru / O.L. Sopronjuk // Nauk. visn. Cherniv. nats. un-tu imeni Jurija Fed'kovycha. Serija: Komp’juterni systemy ta komponenty. — Chernivtsi: ChNU, 2013. — T. 3, vyp. 1. — S. 42–48.

Sopronjuk O.L. Otsinjuvannja dopuskiv na parametry u dyskretnykh dynamichnykh systemakh zi zminoju vymirnosti fazovoho prostoru / O.L. Sopronjuk // Nauk. visn. Cherniv. nats. un-tu imeni Jurija Fed'kovycha. Serija: Komp’juterni systemy ta komponenty. — 2014. — T. 5, vyp. 1. — S. 81–86.

Sopronjuk O.L. Pro rozrakhunok dopuskiv na parametry linijnykh dynamichnykh system zi zminnoju vymirnistju fazovoho prostoru / O.F. Shvets' // Visn. Kyyiv. nats. un-tu imeni Tarasa Shevchenka. Serija: Fizyko-matematychni nauky. — 2015. — № 1. — S. 181–188.

Published

2016-09-26

Issue

Section

Mathematical methods, models, problems and technologies for complex systems research