Modal synthesis method for norm computation of \(H_\infty\) decentralized control systems. II (Q1890255)

When using \(H_\infty\) techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using \(H_\infty\) control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which \(H_\infty\) decentralized control theory corresponds to substructural modal synthesis theory so that the optimal \(H_\infty\) 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 \(H_\infty\) norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems \(H_\infty\) control are presented in part (I) of the paper. The modal synthesis method for computation of the optimal \(H_\infty\) norm of decentralized control systems and numerical examples are presented in part (II).