Enhancing the settling time estimation of a class of fixed-time stable systems

TL;DR

This paper improves the estimation of settling time for fixed-time stable systems by providing a less conservative upper bound, introducing a new predefined-time convergence algorithm, and designing controllers with guaranteed settling times.

Contribution

It offers a new non-conservative upper bound for settling time, proposes a predefined-time convergence algorithm, and designs controllers with guaranteed settling times.

Findings

New less conservative upper bound for settling time

Predefined-time convergence algorithm with a priori settling time

Simulation results show improved performance over existing methods

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 fourfold. First, we revisit the well-known class of fixed-time stable systems, given in (Polyakov et al.,2012}, while 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. Third, 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. At last, predefined-time controllers for first order and second order systems are introduced. Some simulation results highlight the performance of the proposed scheme in terms of settling time estimation compared to existing methods.