Finite-Time Stabilization of Linear Systems by Reduced-Order and Dual Observer-Based Bounded Time-Varying Output Feedback

This article studies the finite-time stabilization of generally controllable and observable linear systems. By exploiting some key properties of the (dual) parametric Lyapunov equation, we design reduced-order and dual observer-based bounded time-varying output feedback, with the explicit time-varying parameters being offline designed, which achieve (prescribed) finite-time stabilization of linear systems. To reduce the regulating time, we propose a second method of solving the control gain parameters, which is solved offline with some scalar differential equations. Compared to the reduced-order observer-based time-varying output feedback, the dual observer-based time-varying output feedback has a smaller dimensionality if the system input dimension exceeds the output dimension. On the contrary, the reduced-order observer-based time-varying output feedback has lower dimensionality. The simulation of aerospace rendezvous systems verified the effectiveness and advantages of the proposed method.