Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Portenko M. S., Melnichuk D. V., Andreichenko D. K. Analyticity Conditions of Characteristic and Disturbing Quasipolynomials of Hybrid Dynamical Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 208-217. DOI: 10.18500/1816-9791-2016-16-2-208-217, EDN: WCNQLZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.06.2016
Full text:
(downloads: 226)
Language: 
Russian
Heading: 
UDC: 
517.935.2
EDN: 
WCNQLZ

Analyticity Conditions of Characteristic and Disturbing Quasipolynomials of Hybrid Dynamical Systems

Autors: 
Portenko Marina Sergeevna, Saratov State University
Melnichuk D. V., Saratov State University
Andreichenko Dmitry Konstantinovich, Saratov State University
Abstract: 

Hybrid dynamical systems (HDS) are connected by means of the boundary conditions and the constraint’s conditions systems of ordinary differential equations and partial differential equations with the corresponding initial conditions. Check the stability of HDS can be performed on the basis of the "fast"algorithm for the application which requires analytic characteristic and disturbing quasipolynomials of HDS in the right half-plane and near the imaginary axis. In this paper we formulate and prove the analyticity conditions of the characteristic and disturbing HDS quasipolynomials. Mathematical models of control objects with distributed parameters in space, matching the thermal conductivity and diffusion processes, the dynamics of support layers of viscous incompressible fluid, as well as the dynamics of the elastically deformable medium taking into account the internal friction.

References: 
  1. Andreichenko D. K., Andreichenko K. P. On thetheory of hybrid dynamical systems. Journal of Computer and Systems Sciences International, 2000, vol. 39, no 3, pp. 383–398.
  2. Andreichenko D. K., Andreichenko K. P. Modelirovanie, analiz i sintez kombinirovannykh dinamicheskikh sistem. Uchebnoe posobie [Modeling, analysis and synthesis of combined dynamical systems. Tutorial]. Saratov, Rait-Ekspo, 2013, 144 p. (in Russian).
  3. Liusternik L. A., Sobolev V. I. Kratkii kurs funktsional’nogo analiza [A short course of functional analysis]. Moscow, Vysshaia shkola, 1982, 271 p. (in Russian).
  4. Andreichenko D. K., Andreichenko K. P. On the theory of stability of a cylindrical hydrodynamic suspension. Fluid Dynamics, 2009, vol. 44, no 1, pp. 10–21.
  5. Andreichenko D. K., Eroftiev A. A., Melnichuk D. V. Parallelization of parametric synthesis by "problems portfolio"scheme based on MPI technology. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2015, vol. 15, no. 2, pp. 222–228 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2015-15-2-222-228.
  6. Andreichenko D. K., Andreichenko K. P., Kononov V. V. On stability theory of autonomous angular stabilization system for combined dynamical systems. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 2, pt. 2, pp. 9–14 (in Russian).
  7. Andreichenko D. K., Andreichenko K. P., Kononov V. V. Parallel algorithm of optimal parameters calculation for the single channel angular stabilization system. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 4, pt. 1, pp. 109–117 (in Russian).
Received: 
12.01.2016
Accepted: 
28.05.2016
Published: 
30.06.2016