Solution 1

(a) Let the signal at the bottom node of the block diagram be denoted by e ( t ). Then we have the following relations

Writing the above equations in Laplace domain, we have

Eliminating the auxiliary signal e ( t ), we get

Hence we get the following differential equation,

(b) From the system function H ( s ) found in the previous part we see that the poles of the system are at s = -1. Since the system is given to be causal, and the right most pole of the system is left of the imaginary axis, the system is stable.