A Class of Continuous Predefined-Time Controllers

A class of continuous predefined-time controllers is designed in this paper. The control structure is built upon a class of comparison functions, whose features allow to analyze the predefined-time convergence property in the Lyapunov framework. Rather than providing exact predefined-time convergence to the equilibrium point, the proposed controller guarantees uniform predefined-time ultimate predefined boundedness of the solutions, i.e., the capability of setting an arbitrarily desired ultimate bound and an arbitrarily desired convergence time, through an appropriate selection of the controller parameters. Moreover, for a class of second-order systems, an additional analysis is carried out to show finite-gain input-output stability. The reliability of the proposed scheme is highlighted through numerical simulations in a representative example.