3. Stability analysis – Frequency-domain methods

Analysis methods can be broadly categorized into two main branches: frequency-domain methods and time-domain methods. The aim of this section is to offer readers insight into various existing frequency-domain methods developed for analyzing linear time-delay systems. This section will primarily focus on techniques applicable analytically to gain fundamental understanding of the stability properties of time-delay systems. Additionally, computational methods suitable for analyzing more complex systems, such as those with large state dimensions or multiple delays, will also be explored.

We will commence with a concise overview of the existing methods, accompanied by corresponding references for comprehensive understanding. Following this, we will describe selected methods in more detail, accompanied by illustrative examples.