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.

Keywords: hybrid systems switched linear systems, switched bilinear systems, realization theory, formal power series, minimal realization

@article{COCV_2011__17_2_446_0, author = {Petreczky, Mih\'aly}, title = {Realization theory for linear and bilinear switched systems: {A} formal power series approach}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {446--471}, publisher = {EDP-Sciences}, volume = {17}, number = {2}, year = {2011}, doi = {10.1051/cocv/2010015}, zbl = {1233.93020}, mrnumber = {2801327}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2010015/} }

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 PY - 2011 SP - 446 EP - 471 VL - 17 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010015/ DO - 10.1051/cocv/2010015 LA - en ID - COCV_2011__17_2_446_0 ER -

%0 Journal Article %A Petreczky, Mihály %T Realization theory for linear and bilinear switched systems: A formal power series approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 446-471 %V 17 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010015/ %R 10.1051/cocv/2010015 %G en %F COCV_2011__17_2_446_0

Petreczky, Mihály. Realization theory for linear and bilinear switched systems: A formal power series approach. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, pp. 446-471. doi : 10.1051/cocv/2010015. http://www.numdam.org/articles/10.1051/cocv/2010015/

[1] Realization and structure theory of bilinear dynamical systems. SIAM J. Control 12 (1974) 517-535. | MR | Zbl

, and ,[2] Nonlinear Control Systems. Springer-Verlag (1989). | MR | Zbl

,[3] Switching in Systems and Control. Birkhäuser, Boston (2003). | MR | Zbl

,[4] Realization theory for bilinear switched systems, in Proceedings of 44th IEEE Conference on Decision and Control (2005). [CD-ROM only.] | Zbl

,[5] Realization Theory of Hybrid Systems. Ph.D. Thesis, Vrije Universiteit, Amsterdam (2006). [Available online at: http://www.cwi.nl/~mpetrec.]

,[6] 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. | Numdam | MR | Zbl

,[7] Realization theory of discrete-time nonlinear systems: Part I - The bounded case. IEEE Trans. Circuits Syst. 26 (1979) 342-359. | MR | Zbl

,[8] Algebraic differential equations and rational control systems. SIAM J. Control Optim. 30 (1992) 1126-1149. | MR | Zbl

and ,*Cited by Sources: *