In control systems, if a system’s transient response is overdamped to a step input, which statement correctly describes its output behavior during the transient period?

Introduction / Context:
Transient response classification (underdamped, critically damped, overdamped) helps predict how systems approach a new steady state after a change such as a step input. Overdamped responses are slow but monotonic, a key property for precision systems where overshoot is unacceptable.

Given Data / Assumptions:

• Input is a step from an initial value to a higher final value.
• System is linear time-invariant with real, negative poles and damping > 1.
• We focus on qualitative behavior (overshoot vs monotonic approach).

Concept / Approach:
An overdamped second-order (or higher-order with dominant real poles) system responds with a sum of decaying exponentials, all positive contributions toward the final value without oscillation. Because there is no oscillatory term, the output rises (or falls) monotonically toward the final value and does not cross it—hence no overshoot.

Step-by-Step Solution:
1) Recall that overshoot arises from oscillatory components (complex poles), absent in overdamped systems. 2) Conclude monotonic convergence toward steady state. 3) Therefore, during the transient, the output never exceeds the final value. 4) Select the option explicitly stating 'no overshoot'.

Verification / Alternative check:
Canonical step-response plots for overdamped systems show a slow, curve-shaped rise without crossing the final value; critically damped touches fastest monotonic, underdamped overshoots and oscillates.

Why Other Options Are Wrong:
Option A: Overshoot is characteristic of underdamped, not overdamped.
Option C: Overdamped systems do stabilize; they may be slow, but they settle.
Option D: Cannot include mutually contradictory statements.
Option E: Incorrect since one statement is true.

Common Pitfalls:
Confusing 'slow' with 'unstable'; overdamped is stable but sluggish, preferred in some safety-critical actuators.

Final Answer:
The output never exceeds the final input value (no overshoot).