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Mathematical Problems in Engineering
Volume 2014, Article ID 635758, 7 pages
http://dx.doi.org/10.1155/2014/635758
Research Article

The Control for Bilinear Systems with Poisson Jumps

1College of Electronic Communication and Physics, Shandong University of Science and Technology, Qingdao 266590, China
2College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
3College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 3 April 2014; Accepted 5 May 2014; Published 21 May 2014

Academic Editor: Xuejun Xie

Copyright © 2014 Rui Zhang 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.

Abstract

This paper discusses the state feedback control problem for a class of bilinear stochastic systems driven by both Brownian motion and Poisson jumps. By completing square method, we obtain the control by solutions of the corresponding Hamilton-Jacobi equations (HJE). By the tensor power series method, we also shift such HJEs into a kind of Riccati equations, and the control is represented with the form of tensor power series.