Small-Time Extinction with Decay Estimate of Bilinear Systems on Hilbert Space

This paper considers the stabilization problem of bilinear systems in small time by various feedback laws. Then, under some reasonable assumptions on the system and control operator, we prove the global polynomial stabilization of the bilinear system, at hand, in a small time by unbounded feedback. A decay rate of the stabilized state is explicitly estimated. Moreover, we use an observability condition to prove a partial stabilization in a prescribed time by time-varying feedback. Examples of heat, transport and wave equations are revisited.

Automated summary

This paper investigates the problem of stabilizing bilinear systems in a short period of time using various feedback laws. With reasonable assumptions on the system and control operator, global polynomial stabilization of the bilinear system is proven in a short time through unbounded feedback. The decay rate of the stabilized state is explicitly estimated. Additionally, a partial stabilization in a prescribed time is achieved through time-varying feedback by utilizing an observability condition. Examples of heat, transport, and wave equations are revisited.