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Let 
be the transfer function of a second-order system. A controller 
is connected to the system 
in the configuration shown below.
Consider the following statements.
(i) There exists no controller of the form 
, where 
is a positive real number, such that the closed loop system is stable.
(ii) There exists at least one controller of the form 
, where 
and 
are positive real numbers, such that the closed loop system is stable.
Which one of the following options is correct?
(i) is TRUE and (ii) is FALSE
(i) is FALSE and (ii) is TRUE
Both (i) and (ii) are FALSE
Both (i) and (ii) are TRUE
Given : 
Characteristic equation: 
Sign change 
(closed Loop system: Unstable)
(ii) 
Characteristic equation: 
Given that 
Real no's
All coefficient +ve in characteristic equation, hence closed loop system is stable.
Hence, correct answer is (D) Both (i) and (ii) are True.