Stability is an important characteristic of a system that determines its behavior over time. A stable system is one that produces bounded output for any bounded input. In other words, if the input to a stable system is limited, the output will also be limited.


The given system h(t) = exp(-7t) is a continuous-time system represented by an exponential function with a negative exponent. To analyze its stability, we need to determine if the system satisfies the conditions for stability.


For a system to be stable, it should produce bounded output for any bounded input. In this case, let's consider a bounded input signal x(t) = A, where A is a constant. Since the input is constant, it is bounded.


To find the output response y(t), we need to convolve the input signal x(t) with the system's impulse response h(t). The convolution operation is given by:
y(t) = ∫[x(τ)h(t-τ)]dτ

In this case, the input signal x(t) is a constant A, and the impulse response h(t) is exp(-7t). Plugging these values into the convolution integral, we get:
y(t) = ∫[A * exp(-7τ) * exp(-7(t-τ))]dτ
= A * ∫[exp(-7t)]dτ

Simplifying the integral, we get:
y(t) = A * [-1/7 * exp(-7t)] + C
= -A/7 * exp(-7t) + C


From the output response y(t) = -A/7 * exp(-7t) + C, we can see that the output is also an exponential function with a negative exponent. As time goes to infinity (t → ∞), the exponential term approaches zero, and the output becomes bounded. Therefore, the output of the system is bounded for any bounded input.


Since the output of the system h(t) = exp(-7t) is bounded for any bounded input, we can conclude that the system is stable. Hence, the correct answer is option 'A' - Yes.