A Decomposition Method for Finite-Time Stabilization of Bilinear Systems with Applications to Parabolic and Hyperbolic Equations

In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time stable without control. This allows the stabilization analysis to focus solely on the remaining subsystem. To ensure the well-posedness of the closed-loop system, we establish sufficient conditions on the system and control operators. The stabilization results are then derived using a suitable Lyapunov function and an observation condition. The effectiveness of the proposed approach is demonstrated through examples involving both parabolic and hyperbolic infinite-dimensional systems.