Suppose we are given the following information about a causal and stable LTI sys-tem S w...

Suppose we are given the following information about a causal and stable LTI sys-tem S with impulse response h(t) and a rational system function H(s):

1. H(1) = 0.2.

2. When the input is u(t), the output is absolutely integrable.

3. When the input is tu(t), the output is not absolutely integrable.

4. The signal is of finite duration.

5. H(s) has exactly one zero at infinity.

Determine H(s) and its reeion of convergence.