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Algorithms having uniform convergence with respect to their initial condition(i.e., with fixed-time stability) are receiving increasing attention forsolving control and observer design problems under time constraints. However,we still lack a general methodology to design these algorithms for high-orderperturbed systems when we additionally need to impose a user-definedupper-bound on their settling time, especially for systems with perturbations.Here, we fill this gap by introducing a methodology to redesign a class ofasymptotically, finite- and fixed-time stable systems into non-autonomousfixed-time stable systems with a user-defined upper-bound on their settlingtime. Our methodology redesigns a system by adding time-varying gains. However,contrary to existing methods where the time-varying gains tend to infinity asthe origin is reached, we provide sufficient conditions to maintain boundedgains. We illustrate our methodology by building fixed-time onlinedifferentiators with user-defined upper-bound on their settling time andbounded gains.

A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time