期刊
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
卷 59, 期 11, 页码 2655-2668出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2012.2190670
关键词
Diffusion; H-infinity synchronization; LMI; N-coupled PDSs; Partial differential systems(PDSs); synchronization
资金
- National Science Council of Taiwan [NSC 99-2745-E-007-001-ASP, NSC 100-2745-E-007-001-ASP]
- National Natural Science Foundation of China [11026189]
- Natural Scientific Research Innovation Foundation in Harbin Institute of Technology [HIT.NSRIF.201014]
In this paper, we address the synchronization problem of coupled partial differential systems (PDSs). First, the asymptotical synchronization and the H-infinity synchronization of N-coupled PDSs with space-independent coefficients are considered without or with spatio-temporal disturbance, respectively. The sufficient conditions to guarantee the asymptotical synchronization and the H-infinity synchronization are derived. The effect of the spatial domain on the synchronization of the coupled PDSs is also presented. Then the problem of asymptotical synchronization of N-coupled PDSs with space-dependent coefficients is dealt with and the sufficient condition to guarantee the asymptotical synchronization is obtained by using the Lyapunov-Krasovskii method. The condition of the H-infinity synchronization for N-coupled PDSs with space-dependent coefficients is also presented. Both conditions are given by integral inequalities, which are difficult to be verified. In order to avoid solving these integral inequalities, we adopt the semi-discrete difference method to turn the PDSs into an equivalent spatial space state system, then the sufficient condition of the H-infinity synchronization for N-coupled PDSs is given by an LMI, which is easier to be verified. Further, the relationship between the sufficient conditions for the H-infinity synchronization, obtained by the Lyapunov-Krasovskii method and semi-discrete difference method respectively, is investigated. Finally, two examples of coupled PDSs are given to illustrate the correctness of our results obtained in this paper.
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