Global asymptotic stabilization of single-input bilinear discrete time-invariant complex systems

The problem of global asymptotic stabilization by state feedback is considered for bilinear autonomous discrete-time control systems with the single input in the complex space. For such systems, the possibility of applying the second Lyapunov method is proved, which is not valid for general nonlinear complex systems. The approach uses the Krasovsky–La Salle theorem on global asymptotic stability for discrete-time systems. Sufficient conditions for global asymptotic stabilization of a bilinear complex system by real state feedback are obtained. Finally, an example of using the obtained results is presented.