On the Predefined, Prescribed and Arbitrary Time Convergence

Over the past few years, rated convergence has gained importance and has acquired tremendous interest from the research community. In this regard, some nomenclatures have emerged, broadly falling under the spectrum of finite time stability. However, these notions have certain aspects which differentiate them. Therefore it becomes imperative to bring out a comparative study among these notions. Moreover, such recent concepts are being applied to several application problems. Thus it is essential to understand even the small details associated with them. The purpose of the present paper is to address these objectives. In addition, the convergence of states and boundedness of the control in case of arbitrary time convergence has also been discussed.