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

ABSTRACT 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.