Global convergence of a class of nonlinear dynamical networks

This paper considers the global convergence of a class of nonlinear dynamical networks, and the subsystems are discrete time pendulum-like systems. Different from most of the existing results, two kinds of interconnections are considered in view of the fact that the subsystems of networks may have more than one kind of interconnection between each other. The 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). The Kronecker product is presented which can be used to handle a class of LMI problems. The test of the global convergence of a network of pendulum-like systems is separated into the test of the global convergence of several independent pendulum-like systems. Furthermore, a controller design method based on LMIs is provided. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.