4. Stability analysis – Time-domain methods

In parallel to frequency-domain methods, time-domain methods offer an alternative for the analysis of time-delay systems. While some of those methods are specific to the time-domain, such as Lyapunov-functional-based approaches, some others are a time-domain reformulation of frequency-domain methods.

There are several advantages for considering time-domain methods over frequency-domain ones: the former can be applied to more general classes of systems such as uncertain, time-varying and nonlinear systems, and they lead to conditions that are easier to verify using computational methods, such as those based on Linear Matrix Inequalities.

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,...