Skip Navigation

IMA Journal of Mathematical Control and Information 2003 20(1):1-19; doi:10.1093/imamci/20.1.1
© 2003 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by El Bouhtouri, A.
Right arrow Articles by El Hadri, K.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Robust stabilization of jump linear systems with multiplicative noise

A. El Bouhtouri1 and K. El Hadri1

1 Département de Mathématiques, Université Chouaib Doukkali, Faculté des Sciences, B.P. 20, El Jadida, Morocco

This paper deals with the robustness of stability and stabilization problem for a class of jump linear systems with Markov jumping parameters and subject to piecewise deterministic and stochastic uncertainties. We prove that the exponential stability of these systems is equivalent to exponential stability of associated linear Itô systems with no jumping parameters subject to structured block-diagonal multi-perturbations. This result is exploited to give lower bounds for what we define as the stability radii of this type of systems, via the resolution of parametrized linear matrix inequalities. The optimization problem by output feedback is also addressed. Sufficient conditions are presented for the existence of a stabilizing dynamic full-order controller, which ensure that the closed-loop system has a stability radius greater than some pre-specified bound, and a procedure for the construction of stabilizing compensator is proposed via the resolution of a number of linear matrix inequalities. The paper ends with a brief discussion of the state feedback case.

Keywords: jump linear systems; Itô systems; structured uncertainties; parametrized linear matrix inequalities; stability radii.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.