ZHONG Wan-xie, WU Zhi-gang, GAO Qiang, A. Y. T. Leung, F. W. Williams. Modal Synthesis Method for Norm Computation of H∞ Decentralized Control Systems (Ⅱ)[J]. Applied Mathematics and Mechanics, 2004, 25(2): 121-127.
 Citation: ZHONG Wan-xie, WU Zhi-gang, GAO Qiang, A. Y. T. Leung, F. W. Williams. Modal Synthesis Method for Norm Computation of H∞ Decentralized Control Systems (Ⅱ)[J]. Applied Mathematics and Mechanics, 2004, 25(2): 121-127.

# Modal Synthesis Method for Norm Computation of H∞ Decentralized Control Systems (Ⅱ)

• Rev Recd Date: 2003-10-08
• Publish Date: 2004-02-15
• When using H techniques to design decentralized controllers for large systems,the whole system is divided into subsystems,which are analysed using H control theory before being recombined.An analogy was established with substructural analysis in structural mechanics,in which H decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H norm of the whole system corresponds to the fundamental vibration frequency of the whole structure.Hence,modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H norm of the control system.The orthogonality and the expansion theorem of eigenfunctions of the subsystems H control are presented in part(Ⅰ) of the paper.The modal synthesis method for computation of the optimal H norm of decentralized control systems and numerical examples are presented in part(Ⅱ).
•  [1] 钟万勰, 吴志刚, 高强，等.H∞分散控制系统范数计算的模态综合法(Ⅰ)[J]. 应用数学和力学, 2004,25(2):111—120. [2] Leung A Y T.Dynamic Stiffness & Sub-Structures[M].London: Springer,1993. [3] 王文亮, 杜作润.结构振动与动力子结构分析[M].上海: 复旦大学出版社, 1985. [4] ZHONG Wan-xie, Williams F W, Bennett P N. Extension of the Wittrick-Williams algorithm to mixed variable systems[J].Journal of Vibration and Acoustics,Transactions of the ASME,1997,119(3): 334—340. [5] ZHONG Wan-xie, Howson W P, Williams F W. H∞ control state feedback and Rayleigh quotient[J].Computer Methods in Applied Mechanics and Engineering,2001,191(3-5): 489—501. [6] Jamshidi M. Large-Scale Systems—Modeling, Control and Fuzzy Logic[M].New Jersey: Prentice-Hall, 1997.

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