Title: On the least upper bound for the settling time of a class of fixed-time stable systems,
Abstract: This paper deals with the convergence time analysis of a class of fixed-time
stable systems with the aim to provide a new non-conservative upper bound for
its settling time. Our contribution is threefold. First, we revisit a
well-known class of fixed-time stable systems showing the conservatism of the
classical upper estimate of the settling time. Second, we provide the smallest
constant that uniformly upper bounds the settling time of any trajectory of the
system under consideration. Then, introducing a slight modification of the
previous class of fixed-time systems, we propose a new predefined-time
convergent algorithm where the least upper bound of the settling time is set a
priori as a parameter of the system. This calculation is a valuable
contribution toward online differentiators, observers, and controllers in
applications with real-time constraints.