Modal synthesis method for norm computation of H ∞ decentralized control systems (I)

Abstract

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>(I) </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 <i>(II)</I>.