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STABILIZATION OF COUPLED PDE-ODE SYSTEMS WITH SPATIALLY VARYING COEFFICIENT

LI Jian , LIU Yungang   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, China.
  • Received:2012-04-16 Online:2013-04-25 Published:2013-07-02
  • Supported by:

    This research is supported by the National Natural Science Foundations of China under Grant Nos. 60974003,61143011, 61273084, and 61233014, the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China under Grant No. JQ200919, and the Independent Innovation Foundation of Shandong University under Grant No. 2012JC014.

LI Jian , LIU Yungang. STABILIZATION OF COUPLED PDE-ODE SYSTEMS WITH SPATIALLY VARYING COEFFICIENT[J]. Journal of Systems Science and Complexity, 2013, 26(2): 151-174.

The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient, via state-feedback or output-feedback. The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve. By infinite-dimensional backstepping method, both state-feedback and output-feedback stabilizing controllers are explicitly constructed, which guarantee that the closed-loop system is exponentially stable in the sense of certain norm. It is worthwhile pointing out that, in the case of output-feedback, by appropriately choosing the state observer gains, the severe restriction on the ODE sub-system in the existing results is completely removed. A simulation example is presented to illustrate the effectiveness of the proposed method.
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