Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

This paper proposes a systematic method to design hierarchical, decentralized, stabilizing controllers for homogeneous hierarchical dynamical networks. Based on LQR approach with a properly chosen performance index including global and local objectives with control input penalty, an obtained optimal LQR feedback gain gives the closed-loop system a prescribed desirable hierarchical structure. In addition, the undesirable eigenvalues of the given homogeneous network can be selectively shifted by further selecting the weighting matrices based on the left eigenvectors associated with those eigenvalues. Finally, the proposed method is summarized into a systematic design procedure with an illustrative numerical example to show its effectiveness.