The question requires matching List I with List II based on control system concepts. Let's explore each option:

1. Graph in List I (a) corresponds to an exponentially decaying signal, which is typically represented by a pole on the negative real axis. This can be matched with ii which is an image showing a pole at \(-1\).

1. Graph in List I (b) represents an exponentially growing signal. This signal matches with i: triple pole at \(s=0\) indicating initial conditions affecting the system indefinitely.

1. Graph in List I (c) is a constant signal, which is a typical response of a stable system with a pole at the origin. This corresponds to iv.

1. Graph in List I (d) represents a sinusoidal response due to imaginary poles. This corresponds to iii, which is a representation of purely imaginary poles.

Thus, the correct matching is:

• a - ii
• b - i
• c - iv
• d - iii

The correct option is a - ii, b - i, c - iv, d - iii.