Stabilization of complex dynamical networks with noise disturbance under performance constraint

Under given performance constraint, this paper studies the stabilization problem of general dynamical network subject to noise disturbance. The newly presented dynamical network model includes both intrinsic disturbance of single node and communication noise over the network connections, which appear typically in a network environment. Single controller is pinned into one of the nodes for the exponential stabilization of dynamical network, and the prescribed performance constraint is satisfied. The reason why only one controller is valid for stabilization of dynamical network is the full utilization of network’s local connections. One important feature of this paper is the introduction of the performance constraint concept into the stabilization of complex dynamical network with intrinsic and communication noises. The derived criteria are expressed in terms of linear matrix inequalities (LMIs), which are easy to be verified by resorting to recently developed algorithm. Numerical example is utilized to illustrate the effectiveness of the proposed results.