Ordinary Differential Equations and Delays

We introduce the two most important class of convolution system, and their transfer functions.

[@mnada72]

Thank you. I very much like the insights you gave on the subject. Is it right to say that if initial conditions are of interest we have to use state space representation while if the initial conditions are not considered we can use Transfer function representation?

[@pawelo2698]

Thank you, However I dont see the effect of this delay in the diagram of the system. I suppose that this is that way: Output Y is based on the input of the system U at time t - . Is it right?

[@richard_pates]

Yes, that's right. A delay means that y(t)=u(t-T), where T is the length of the delay. In the picture we try to rewrite this equation in terms of a relationship between the Laplace transforms of y(t) and u(t). Doing this we find that Y(s)=exp(-sT)U(s), so for a delay, the G(s) in the picture is equal to exp(-sT)