Global exact prescribed-time output feedback stabilization of a class of nonlinear systems with measurement uncertainty by linear time-varying feedback

This article addresses the global exact prescribed-time output feedback stabilization problem for a class of nonlinear systems subject to measurement uncertainty and unknown nonlinearities. Unlike many prescribed-time control results, where the theoretical analysis does not exclude the possibility of convergence before the prescribed time, the exact prescribed-time convergence considered in this paper further characterizes the non-premature convergence: nonzero closed-loop trajectories approach the origin at the prescribed time in the limiting sense and do not vanish before that time. To achieve this guarantee, the proposed approach employs the solutions of the parametric Lyapunov equations (PLEs) as the central analytical tool and fully exploits their properties, in conjunction with time-varying Lyapunov-like functions, to construct a linear observer-based output feedback control strategy. A salient feature of the proposed scheme is that it relies exclusively on linear time-varying gains. Finally, two numerical case studies, including comparisons with existing methods, are provided to demonstrate the effectiveness of the proposed approach.