On the design of new classes of predefined-time stable systems: A time-scaling approach.

A methodology, based on time-scale transformations and Lyapunov analysis, for designing autonomous and non-autonomous dynamical systems exhibiting the predefined-time stability property is provided in this paper. Thus, the current proposal allows characterizing a broad class of predefined-time stable systems, placing them under a common framework with existing methods which use time-varying gains based on time-base generators. What follows from this construction is that the bound of the convergence time for this class of systems is the lowest possible. Moreover, it is independent of the initial conditions and is set \textit{a priori} through a tuning parameter. This design procedure is a relevant contribution when compared to traditional fixed-time convergent algorithms since the current convergence time bounds are conservative. Finally, we analyze several existing and novel algorithms for autonomous and non-autonomous systems showing the effectiveness of the method.