@Inbook{Aldana-López2023,
author="Aldana-L{\'o}pez, Rodrigo
and Seeber, Richard
and Haimovich, Hernan
and G{\'o}mez-Guti{\'e}rrez, David",
editor="Oliveira, Tiago Roux
and Fridman, Leonid
and Hsu, Liu",
title="Designing Controllers with Predefined Convergence-Time Bound Using Bounded Time-Varying Gains",
bookTitle="Sliding-Mode Control and Variable-Structure Systems: The State of the Art",
year="2023",
publisher="Springer International Publishing",
address="Cham",
pages="37--67",
abstract="Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers.",
isbn="978-3-031-37089-2",
doi="10.1007/978-3-031-37089-2_3",
url="https://doi.org/10.1007/978-3-031-37089-2_3"
}