Correct Answer - Option 1 : Asymptotically stable
Asymptotically stable:
A system is defined to be exponentially stable if the system response decays exponentially towards zero as time approaches infinity. For linear systems, uniform asymptotic stability is the same as exponential stability.
If output tends towards zero in absence of input, the system is said to be asymptotically stable.
Important Points:
The stability of a linear closed-loop system can be determined from the locations of closed-loop poles in the S-plane.
Stable System: If all the roots of the characteristic equation lie on the left half of the 'S' plane then the system is said to be a stable system.
Marginally Stable System:
- A linear time-invariant system is said to be critically or marginally stable if for a bounded input its output oscillates with constant frequency & Amplitude.
- Such oscillation of output is called Undamped or Sustained oscillations. For such a system, one or more pairs of non-repeated roots are located on the imaginary axis.
Unstable System:
- If any or all the roots of the system lie on the left half of the 'S' plane then the system is said to be an unstable system.
- Also, if there are repeated poles located purely on the imaginary axis, then the system is said to be unstable.
