Static output controller design for consensus of dynamical networks with interconnections

This paper considers the consensus problems for complex dynamical network systems. For the dynamical network systems, more than one interconnections are considered in view of the fact that the subsystems of networks may be multiple interconnected. Sufficient and necessary conditions for consensus are given for the linear dynamical networks with state interconnections and controller interconnections. Moreover, a static output controller design method based on a parameter-dependent Lyapunov function is provided. Furthermore, multiple interconnected nonlinear dynamical network system is investigated, and the subsystems are Lure systems. Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel criteria, which have the forms of linear matrix inequalities (LMIs). And the test of the consensus of a network with Lure systems as its nodes is separated into the test of the absolute stability of several independent Lure systems. Finally, numerical examples are presented to illustrate the efficiency and applicability of the proposed methods.