Question

The system given by equation y(t-2a)-3y(t-a)+2y(t)=x(t-a) is?​

Answer 1

Answer:

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Answer 2

Answer:

Given, y(t-2a)-3y(t-a)+2y(t)=x(t-a), then

Taking Laplace transform, e-2as Y(s)-3e-as Y(s)+2Y(s)=e-as X(s),

Hence, H(s)=e−as/(1−e−as)(2−e−as)

To find the stability, we should have, ∫∞−∞H(s)ds>0

Hence, ∫∞−∞e−as/(1−e−as)(2−e−as)ds

Let, e−as=z

=>−ae−as ds=dz

It is stable.

The system given by equation y(t-2a)-3y(t-a)+2y(t)=x(t-a) is stable.