If the systems\' transfer function is represented by the following zero-pole dia
ID: 2083467 • Letter: I
Question
If the systems' transfer function is represented by the following zero-pole diagram. What statement best describes the stability of this system? The system is unstable, since some of its poles are in the left-hand s-plane The system is stable, since all its zeros are in the left-hand s-plane The system is stable, since all its poles are in the left-hand s-plane The system is unstable, since some of its zeros are in the right-hand s-plane The system is unstable, since some of its zeros are in the left-hand s-plane The system is stable, since some of its poles are in the left-hand s-plane The system is stable, since some of its zeros are in the left-hand s-plane The system is unstable, since some of its poles are in the right-hand s-plane The system is stable, since some of its poles are in the right-hand s-plane The system is unstable, since all its poles are in the left-hand s-plane The system is unstable, since all its zeros are in the left-hand s-plane The stability of this system cannot be determinedExplanation / Answer
The system is unstable because some of it's poles are in the right hand s-plane.
Explanation - system having pole in right half will have the term g(s)/(s-a). The partial fraction of this type of transfer function will contain a term A/(s-a) and the inverse tranform of this will be Aexp(at)u(t). Since pole is in right half plane, a > 0 and the exp(at) will keep on increasing with increase in time. Thus ooutput of the system will not be bounded. Hence the pole in right half s-plane forces system towards unstability. For pole in the left half s-plane, the exponential will decrease with increase in time and response will be bounded. The above is not true for right half zero as the system having zero in right half plane may not be always unstable (But in the above question, there is no zero in right half plane).
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