Dichotomy and Absolute Stability Analysis of a Class of Complex Dynamical Networks

This paper deals with dichotomy and absolute stability problem for a class of complex network systems with each node be a general Lur’e system which has sector constraint functions. The interconnections of complex network systems referred in this paper conclude not only the linear interconnection of states, but also the interconnection of the sector nonlinearities. Besides, bilinear matrix inequality (BMI) conditions of dichotomy and absolute stability of complex network systems are derived. Moreover, controller design methods of dichotomy and absolute stability of complex system are given in this paper and the related controller can be constructed via feasible solutions of a certain set of bilinear matrix inequalities (BMIs). Finally, examples are given to illustrate the effectiveness of the proposed methods.