Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T15:06:30.887Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part II: Bilinear switched systems*

Published online by Cambridge University Press:  31 March 2010

Mihály Petreczky
Mihály Petreczky*
Affiliation:
Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands. [email protected].
Get access

Abstract

This paper is the second part of a series of papers dealing withrealization theory of switched systems.The current Part II addresses realization theory of bilinear switchedsystems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realizationtheory of linear switched systems.More precisely, in Part II we present necessary and sufficient conditionsfor a family of input-output maps to berealizable by a bilinear switched system, together with a characterizationof 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 isadmissible, but within this restricted set the switching times are arbitrary.The paper uses the theory of formal power series to derivethe results on realization theory.

Keywords

Hybrid systems switched linear systemsswitched bilinear systemsrealization theoryformal power seriesminimal realization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 446 - 471
Copyright
© EDP Sciences, SMAI, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

D'Alessandro, P., Isidori, A. and Ruberti, A., Realization and structure theory of bilinear dynamical systems. SIAM J. Control 12 (1974) 517–535. CrossRef
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: http://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: 10.1051/cocv/2010014.
Sontag, E.D., Realization theory of discrete-time nonlinear systems: Part I – The bounded case. IEEE Trans. Circuits Syst. 26 (1979) 342–359. CrossRef
Wang, Y. and Sontag, E., Algebraic differential equations and rational control systems. SIAM J. Control Optim. 30 (1992) 1126–1149. CrossRef