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

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

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

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topPetreczky, 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

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

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