Stability

Stability

1. By: Abigail Romero Trejo

   • 1112567

2. A stable system has a bounded response to a bounded input

3. Absolute stability: whether the system is either stable or unstable

   • All poles of the transfer function must have a negative real values
     • The poles will lie in the left-half s plane
   • LTI system (Linear Time-Invariant)
     • It is stable if the output evetually comes back to its equilibrium state when the system is subjected to an initial condition
     • It is unstable if the output diverges without bound from its equilibrium state when the system is subjected to an initial condition
     • It is marginally stable if the natural response neither decays nor grows but remains constant or oscillates as time approaches to infinity

4. Relative stability: The degree of stability of the system acording to the value of a parameter

5. It is determined by the poles

   • The response is bounded if the poles are negative

6. How to know if the system is stable without solving the polynomial equation:

   • One way is Routh´s Stability Criterion
   • If you want to get to know about relative stability, just substitute "Ŝ - σ " instead of "S"
     • Where σ is a displacement magnitude

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