  This paper aims to introduce a design methodology to stabilize a chain of
integrators in a fixed-time with predefined Upper Bound for the Settling-Time
(UBST). This approach is based on time-varying gains (time-base generator) that
become singular as the time approaches the predefined convergence time. We
present the conditions such that every nonzero trajectory convergence exactly
at the predefined time with feedback laws that are simpler than in previous
approaches. Additionally, we present results such that the origin is reached
before the singularity occurs, making this approach realizable in practice. A
significant contribution, since current results, based on time-varying gains,
required the time-varying gain to tend to infinity as the time approaches the
prescribed/predefined-time.
  Moreover, our approach guarantees fixed-time convergence with predefined UBST
even in the presence of bounded disturbances (with known bound) and provides a
methodology to re-design an autonomous fixed-time controller where the estimate
of the UBST for the closed-loop system is very conservative into a less
conservative one with predefined \textit{UBST} that can be set arbitrarily
tight. We present numerical examples to illustrate the effectiveness of the
approach together with comparisons with existing autonomous fixed-time
controllers.
