Abstract and Applied Analysis
Volume 2004 (2004), Issue 6, Pages 487-499

Efficient criteria for the stabilization of planar linear systems by hybrid feedback controls

Elena Litsyn,1 Marina Myasnikova,2 Yurii Nepomnyashchikh,2 and Arcady Ponosov3

1Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
2Department of Mechanics & Mathematics, Perm State University, 15 Bukirev Street, Perm 614990, Russia
3Institutt for Matematiske Fag, Norges Landbrukshøgskole (NLH), Postboks 5035, N-1432 Ås, Norway

Received 20 September 2002

Copyright © 2004 Elena Litsyn et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We suggest some criteria for the stabilization of planar linear systems via linear hybrid feedback controls. The results are formulated in terms of the input matrices. For instance, this enables us to work out an algorithm which is directly suitable for a computer realization. At the same time, this algorithm helps to check easily if a given linear 2×2 system can be stabilized (a) by a linear ordinary feedback control or (b) by a linear hybrid feedback control.