Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 2, page 446-471
  • ISSN: 1292-8119

Abstract

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This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal realizations. Similarly to Part I, the paper deals with two types of switched systems. The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory.

How to cite

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Petreczky, Mihály. "Realization theory for linear and bilinear switched systems: A formal power series approach." ESAIM: Control, Optimisation and Calculus of Variations 17.2 (2011): 446-471. <http://eudml.org/doc/197332>.

@article{Petreczky2011,
abstract = { This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal realizations. Similarly to Part I, the paper deals with two types of switched systems. The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory. },
author = {Petreczky, Mihály},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hybrid systems switched linear systems; switched bilinear systems; realization theory; formal power series; minimal realization; hybrid systems; switched linear systems; switched bilinear systems; formal power series},
language = {eng},
month = {5},
number = {2},
pages = {446-471},
publisher = {EDP Sciences},
title = {Realization theory for linear and bilinear switched systems: A formal power series approach},
url = {http://eudml.org/doc/197332},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Petreczky, Mihály
TI - Realization theory for linear and bilinear switched systems: A formal power series approach
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/5//
PB - EDP Sciences
VL - 17
IS - 2
SP - 446
EP - 471
AB - This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal realizations. Similarly to Part I, the paper deals with two types of switched systems. The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory.
LA - eng
KW - Hybrid systems switched linear systems; switched bilinear systems; realization theory; formal power series; minimal realization; hybrid systems; switched linear systems; switched bilinear systems; formal power series
UR - http://eudml.org/doc/197332
ER -

References

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  1. P. D'Alessandro, A. Isidori and A. Ruberti, Realization and structure theory of bilinear dynamical systems. SIAM J. Control12 (1974) 517–535.  
  2. A. Isidori, Nonlinear Control Systems. Springer-Verlag (1989).  
  3. D. Liberzon, Switching in Systems and Control. Birkhäuser, Boston (2003).  
  4. M. Petreczky, Realization theory for bilinear switched systems, in Proceedings of 44th IEEE Conference on Decision and Control (2005). [CD-ROM only.]  
  5. M. Petreczky, Realization Theory of Hybrid Systems. Ph.D. Thesis, Vrije Universiteit, Amsterdam (2006). [Available online at: .]  URIhttp://www.cwi.nl/~mpetrec
  6. M. Petreczky, Realization theory linear and bilinear switched systems: A formal power series approach – Part I: Realization theory of linear switched systems. ESAIM: COCV (2010) DOI: .  DOI10.1051/cocv/2010014
  7. E.D. Sontag, Realization theory of discrete-time nonlinear systems: Part I – The bounded case. IEEE Trans. Circuits Syst.26 (1979) 342–359.  
  8. Y. Wang and E. Sontag, Algebraic differential equations and rational control systems. SIAM J. Control Optim.30 (1992) 1126–1149.  

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