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Mathematical Problems in Engineering
Volume 2013, Article ID 902452, 11 pages
Research Article

Observer-Based Stabilization of Spacecraft Rendezvous with Variable Sampling and Sensor Nonlinearity

1Research Center of Satellite Technology, Harbin Institute of Technology, Harbin 150001, China
2Department of Engineering, Faculty of Technology and Science, University of Agder, 4898 Grimstad, Norway

Received 10 July 2013; Accepted 19 August 2013

Academic Editor: Hongli Dong

Copyright © 2013 Zhuoshi Li 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.


This paper addresses the observer-based control problem of spacecraft rendezvous with nonuniform sampling period. The relative dynamic model is based on the classical Clohessy-Wiltshire equation, and sensor nonlinearity and sampling are considered together in a unified framework. The purpose of this paper is to perform an observer-based controller synthesis by using sampled and saturated output measurements, such that the resulting closed-loop system is exponentially stable. A time-dependent Lyapunov functional is developed which depends on time and the upper bound of the sampling period and also does not grow along the input update times. The controller design problem is solved in terms of the linear matrix inequality method, and the obtained results are less conservative than using the traditional Lyapunov functionals. Finally, a numerical simulation example is built to show the validity of the developed sampled-data control strategy.