Delayed Positive Feedback Can Stabilize Oscillatory Systems

Abstract

This paper expands on a method proposed in [1] for stabilising oscilatory system with positive, delayed feedback. The dosed-loop sytem obtained is shown (using the Nyquist criterion) to be stable for a range of delays.

Graphical Stabilization Approach for Unstable First Order Linear Systems with Time Delay

“…For example, a new LyapunovKrasovskii functional is introduced to take into account that a nominal delay may be different from zero. Also, as it has been shown in [3,4,5,6] and references therein, there exist systems that are unstable in the case free of delays and becomes stable only for some strictly positive values of the delay. In [7], the observer based approach is considered for stabilization and control of unstable first-order plants with known parameters.…”

Controlling across complex networks – Emerging links between networks and control

“…In (Morse, 2006) the composition properties of graphs are used to show that under certain assumptions on the communication topology, delays have no effect on the stability of the system. In fact, in a somehow counterintuitive situation, it turns out that longer delays (if used judiciously) can improve the stability of some systems (Abdallah et al, 1993).…”

Global existence and energy decay of solutions to a Bresse system with delay terms

“…Let us introduce the semigroup representation of the Bresse system (8) and (9). Let U = (ϕ, ϕ t , z 1 , ψ, ψ t , z 2 , ω, ω t , z 3 )…”

“…Whenever material, information or energy is physically transmitted from one place to another, there is a delay associated with the transmission. In recent years, the PDEs with time delay effects have become an active area of research and arise in many pratical problems (see for example [9], [10]). The presence of delay may be a source of instability.…”