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Mathematical Problems in Engineering - Volume 2015 2015, Article ID 152410, 7 pages -

Research Article

College of Engineering, Bohai University, Jinzhou, Liaoning 121013, China

Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

College of Information Science and Technology, Bohai University, Jinzhou, Liaoning 121013, China

Received 22 September 2014; Accepted 5 December 2014

Academic Editor: Guangming Xie

Copyright © 2015 Xing Xing 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.


The problem of switching stabilization for a class of switched positive nonlinear systemsswitched positive homogeneous cooperative system SPHCS in the continuous-time context and switchedpositive homogeneous order-preserving system SPHOS in the discrete-time context is studied by usingaverage dwell time ADT approach, where the positive subsystems are possibly all unstable. To tacklethis problem, a new class of ADT switching is first defined, which is different from the previous definedADT switching in the literature. Then, the proposed ADT is designed via analyzing the weighted norm of the considered system’s state. A sufficient condition of stabilization for SPHCSs with unstablepositive subsystems is derived in continuous-time context. Furthermore, a sufficient condition for SPHOSsunder the assumption that all modes are possibly unstable is also obtained. Finally, a numerical exampleis given to demonstrate the advantages and effectiveness of our developed results.

Author: Xing Xing, Zhichun Jia, Yunfei Yin, and Tingting Wu



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