Stability Analysis of Complex-valued Globally Projected Dynamical Systems

The globally projected dynamical system is a type of dynamical system constructed by the projection operator, which can be applied to solve some nonmonotone variational inequalities and constrained optimization problems. In this paper we extend the globally projected dynamical system to the complex domain and study the dynamical behaviors of the complex-valued globally projected dynamical system. By using energy-like function, Lyapunov stability method, space decomposition approach and inequality technique, the stability of linear and nonlinear complex-valued globally projected dynamical systems is studied. The simulation result shows the effectiveness of the obtained results.