Feedback Stabilization of Bilinear Systems

This monograph explores feedback stabilization of bilinear control systems evolving in Hilbert and Banach spaces, with particular emphasis on unbounded control operators arising in PDE models. It develops a unified and comprehensive framework for weak, strong, robust, and exponential stabilization, incorporating nonlinear feedback laws, such as homogeneous, normalized, and switching feedbacks. By combining tools from functional analysis, semigroup theory, and control theory, this book bridges linear and nonlinear stabilization strategies and highlights the robustness of feedback mechanisms in infinite-dimensional systems. Feedback Stabilization of Bilinear Systems will serve as an ideal resource for researchers, graduate students, and practitioners who seek deeper insight into the stabilization of PDE-governed systems as well as applications where bilinear dynamics naturally arise.