Stability of System


Stability of system

In linear time invariant system we have:
1.    If input is zero output also zero.
2.    It should be independent of any non linear operator like square , cube ,root, sine, log etc. on either input side or output side.
3.    Differential operator is linear operator. 
There should not be any time scaling i.e. coefficient should be  independent of time.

Stability of LTI system may be defined as :
 When system is subjected to bounded input output must be bounded. That is it must follow the BIBO (bounded input and bounded output) criterion.
The stability of system is depends upon roots of characteristics equation i.e.                    1+G(s) *H(s) = 0

A.    Addition of pole always results in stability.
B.    Addition of zero results in stability.

Effect of Feedback on Stability

A system is said to be stable, if its output is under control. Otherwise, it is said to be unstable.
In Equation 

 if the denominator value is zero (i.e., GH = -1), then the output of the control system will be infinite. So, the control system becomes unstable.

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