Metzler asymptotic stability of initial time linear time-varying real-order systems

Abstract

Determining the asymptotics of many time-varying systems associated with real orders remains a challenging issue in qualitative asymptotic theory. This paper introduces a new concept of Metzler asymptotic stability to linear time-varying real-order systems. The design class is considered in standard and block matrix forms whenever the initial time is defined on the real axis. The non-negativity of such systems is discussed by introducing a time-dependent Metzler matrix. New theoretical conditions are developed that guarantee the asymptotic stability of such systems. It is shown that, to ensure the Metzler asymptotic stability of such systems; it suffices to construct a suitable linear non-negative asymptotic stable system where the coefficient matrix should be Metzler. Examples illustrate the potential practical and promising applicability of the introduced results.