On the global finite-time stabilization of bilinear systems by homogeneous feedback laws. Applications to some PDE's

In this paper, the problem of global finite-time stabilization of bilinear control systems by means of homogeneous feedback law is investigated. We prove under some reasonable assumptions on the operators A and B that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite-time the closed loop system. For illustrative, the examples of heat, Schrodinger and transport equations are considered where homogeneous stabilizing feedback is built for these systems. (C) 2019 Elsevier Inc. All rights reserved.