The aim of the project is to find new procedures and methods that allow the efficient synchronization and the decentralized control of complex networks, especially the elimination of some influences, for example, the time delays, quantization, change of the behavior of nodes, loss of connection, etc. The problem of decentralized control and synchronization properties using the so-called Laplacian, adaptive control of complex networks, including chaotic networks will be solved. Conditions ensuring the stability of the specific network, depending on their topology will be investigated as well. Another interesting problem for research is associated with generalization of the spectral properties of more Laplacians with respect to the rate of convergence in directed complex networks and their robustness properties. An integral part of the proposed research will also analyze the possible outcomes for the further application-oriented research on the reliability of power grids, smart grids and other topics within the priority directions of the research in the Czech Republic.