Prescribed Finite Time Stabilization of Linear Systems With State Constraints

This paper studies the prescribed finite time stabilization control problem of multi-input linear control systems subject to uncertainties and state constraints. Different from finite-time and fixed-time control methods, a novel switching nonsingular coordinate transformation function based on the block decomposition technique is developed, resulting in a solution that the control action is continuous and bounded based on the transformed system. Moreover, the boundedness of closed-loop system states is ensured with prescribed finite time performance. Furthermore, we incorporate the barrier Lyapunov function into the stabilization control design to restrain the amplitudes of system states. Numerical examples are provided to verify the effectiveness of the proposed prescribed finite time control strategy.