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.

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Published

2016-09-26

Issue

No. 3 (2016)

Section

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

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