Complete stability for neutral time-delay systems: A unified frequency-sweeping approach

Abstract

This paper studies the complete stability of time-delay systems of neutral type (shortly, neutral systems), inspired by that the complete stability of time-delay systems of retarded type (shortly, retarded systems) was recently solved by establishing a new frequency-sweeping (mathematical) framework. It is not hard to see that the invariance property, the most important basis for building up the frequency-sweeping framework for retarded systems, also holds for neutral systems. We are hence motivated to apply the relevant results to neutral systems by considering the distinctions between two types of time-delay systems. It will be interesting to see that these distinctions can be effectively covered in the frequency-sweeping framework. More precisely, we will find: (1) the stability of the neutral operator (as a necessary stability condition additionally required by neutral systems) can be directly examined from the frequency-sweeping curves (FSCs); and (2) the ultimate stability problem for neutral systems can be fully studied from the FSCs. As a consequence, the frequency-sweeping framework is proved to be also a unified approach for the complete stability of neutral time-delay systems.