Lambert W function

#Control #delay The Lambert W function is a strong mathematical tool that helps us study linear time-delayed systems.

Consider the system below: \(\dot{x} = A x(t) + A_d x(t - \tau)\) Studying this system is not as straightforward. This system has infinitely many eigenvalues, and its stability depends on $A$, $A_d$ and $\tau$. This is called a linear time-delayed system.