What kinds of system can be used as tracking-differentiator

Abstract

A survey of several kinds differentiators is given firstly. The comparison shows the tracking-differentiator (TD) permits a weaker condition on the stabililty of the systems, which can be used to construct differentiators. Moreover, TD sets some weaker constraints on the input signal. Then the paper gives the proofs for two kinds of systems that can be used to construct TD: one is the semi-globally finite time stable autonomous system, a more general kind is the one whose certain time-scale transform is uniformly semi-globally practically asymptotically stable.