  This paper aims to provide a methodology for generating autonomous and
non-autonomous systems with a fixed-time stable equilibrium point where an
Upper Bound of the Settling Time (UBST) is set a priori as a parameter of the
system. In addition, some conditions for such an upper bound to be the least
one are provided. This construction procedure is a relevant contribution when
compared with traditional methodologies for generating fixed-time algorithms
satisfying time constraints since current estimates of an UBST may be too
conservative. The proposed methodology is based on time-scale transformations
and Lyapunov analysis. It allows the presentation of a broad class of
fixed-time stable systems with predefined UBST, placing them under a common
framework with existing methods using time-varying gains. To illustrate the
effectiveness of our approach, we generate novel, autonomous and
non-autonomous, fixed-time stable algorithms with predefined least UBST.
