Journal Article

Finite and infinite horizon <i>H</i><sub>∞</sub> control for stochastic nonlinear systems

M. D. S. ALIYU and E. K. BOUKAS

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 3, pages 265-279
Published in print September 2000 | ISSN: 0265-0754
Published online September 2000 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/17.3.265
Finite and infinite horizon H∞ control for stochastic nonlinear systems

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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

Journal Article.  0 words. 

Subjects: Mathematics

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