Global asymptotic stabilization of time-invariant bilinear non-homogeneous complex systems

The problem of global asymptotic stabilization by state feedback is considered for time-invariant bilinear non-homogeneous control systems 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 Barbashin-Krasovsky theorem on global asymptotic stability. Sufficient conditions for global asymptotic stabilization of a bilinear non-homogeneous complex system by real state feedback are obtained. Finally, an example of using the obtained results is presented.