Journal Article

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


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:
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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