A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller makes use of the information on the corresponding node's dynamics and the resulting overall controller is composed of those sub-controllers. The overall controller can be obtained by means of a combination of typical control designs and appropriate parametric tuning for each isolated node. Several numerical simulation examples are given to illustrate the feasibility and the efficiency of the proposed control design.
We show how we can transform the H∞ and H2 control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for H∞ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal H2 controller.