Global asymptotic stabilization of autonomous bilinear complex systems

Abstract

We consider bilinear autonomous control systems in the complex space. To solve the problem of stabilization of these systems, we apply the method of Lyapunov functions to complex-valued systems. The Jurdjevic–Quinn approach is used which is based on the Barbashin–Krasovsky–La Salle theorem on global asymptotic stability. We obtain sufficient conditions for global asymptotic stabilization of a bilinear complex system by real state feedback. Finally, examples of using the obtained results are presented.