Consider the transfer function YsUs 2ss 2 Is the system BI

Consider the transfer function: Y(s)/U(s) = 2/s(s + 2) Is the system BIBO stable? If not, find a bounded input that leads to an zero initial conditions.

Solution

The function Y(s) = 2/[s*s+2*s] is less than 2/3 for all s >1. For all other s /=0 the function is less than infinity.

In fact if the input is bounded, the output is bounded.

Now 2/s(s+2) = 1/s - 1/(s+2)

the inverse laplace transform of 1/s ia 1

the inverse LT of 1/s+2 is exp -(at)

The constant is bounded, the exponential is bounded as the power is negative.

HENCE BIBO

he inverse transform of 1/s

T