Stability, Delays and Multiple Characteristic Roots in Dynamical Systems: A Guided Tour

This paper presents a guided tour of some specific problems encountered in the stability analysis linear dynamical systems including delays their systems' representation. More precisely, we will address characterization multiple roots corresponding characteristic function with particular emphasis on way these are affected by system's parameters and that they can be used to control. The covers several approaches (perturbation techniques, hypergeometric functions) leading methods criteria (frequency-sweeping, multiplicity-induced-dominancy) implemented (software toolboxes) for analyzing qualitative quantitative properties induced other dynamics. A attention paid so-called partial pole placement method based multiplicity-induced-dominancy property. presentation is as simple possible, focusing more main intuitive ideas appropriate mathematical reasoning analogy theoretical results well potential use practical applications. Illustrative examples complete paper.