Output finite-time stabilisation of a class of linear and bilinear control systems

Based on the idea of Lyapunov function, we investigate the output finite-time stability of some classes of abstract bilinear systems using feedback control laws. We first design a stabilising feedback control. Then, we study the well-posedness of the system in closed-loop by using the theory of maximal monotone operators. Then we proceed to the question of output finite-time stability in a settling time of the system at hand. The obtained results are also applied to derive output finite time stabilisation results for linear systems. The algorithm of feedback control design is further applied to finite dimension systems and also to PDE of parabolic and hyperbolic types.