Prescribed‐Time Fault‐Tolerant Control of Linear Time‐Varying Systems by Linear Time‐Varying Feedback

ABSTRACT In this paper, the prescribed‐time fault‐tolerant control for multiple input multiple output (MIMO) linear time‐varying (LTV) systems is investigated. Both lexicographically fixed and non‐lexicographically fixed LTV systems have been considered. By leveraging the special structure of the controllable canonical form and employing the properties of the parametric Lyapunov equation, a global prescribed‐time fault‐tolerant controller is designed. With the aid of a suitable Lyapunov‐like function, it is demonstrated that the state can converge to zero within the prescribed time. The convergence time is independent of the initial condition. In addition, the designed controller is continuous, bounded, and even maintains a linear and concise form. Ultimately, the effectiveness of the controller is verified through the simulation of the elliptical orbital rendezvous system.