Skip Navigation

IMA Journal of Mathematical Control and Information 2000 17(3):265-279; doi:10.1093/imamci/17.3.265
© 2000 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 ALIYU, M. D. S.
Right arrow Articles by BOUKAS, E. K.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Finite and infinite horizon H{infty} control for stochastic nonlinear systems

M. D. S. ALIYU1 and E. K. BOUKAS2 {dagger}

1Systems Engineering Department, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia
2Mechanical Engineering Department, École Polytechnique de Montréal, ‘Center-ville’, P.O. Box 6079, station, Montréal, Québec, Canada H3C 3A7

In this paper, the problem of disturbance attenuation with internal stability for nonlinear systems with Markovian jumping parameters is considered. It is shown that this problem is solvable if there exists a sequence of smooth-positive semidefinite functions satisfying certain Hamilton-Jacobi-Isaac equations (inequalities). Furthermore, it is shown that, if this solution exists, it represents a stochastic Lyapunov function for the closed-loop nonlinear system. A parametrization of the family of full-information state-feedback controllers satisfying the disturbance-attenuation requirement with stochastic stability for the closed-loop system is also given.

Keywords: nonlinear system; Markov jump process; dissipative system; disturbance attenuation; stochastic stability.

{dagger} Email: boukas{at}anas.meca.polymtl.ca


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.