Designated‐time stabilizing strategy for a class of time‐varying nonlinear systems and its application to pendulum system

Abstract

In this paper, a new scheme is proposed to stabilize a class of nonlinear systems within a designated time, mainly motivated by two unsolved problems: the singularity caused by infinity control magnitudes at the prescribed time instant and the lack of formulating/manipulating state responses after the prescribed time. Under the proposed scheme, an exquisite controller is constructed by entailing both the state scaling approach and a finite‐time stabilizing procedure. It is shown that the obtained control is well defined with bounded magnitude on the whole‐time horizon and ensures the existence of the solutions of the closed‐loop system. Superior to the existing prescribed time stabilization results, the proposed method is capable of ensuring that the states of the closed‐loop system converge to a small compact set within the designated time, stay inside it thereafter and perform finite‐time convergence eventually. Simulation examples are presented to illustrate the effectiveness of the proposed approach.