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Consider a system where 
, and 
are three internal state signals and 
is the input signal. The differential equations governing the system are given by
Which of the following statements is/are TRUE?
The signals , and are bounded for all bounded inputs
There exists a bounded input such that at least one of the signals 
, 
, and is unbounded
There exists a bounded input such that the signals , and are unbounded
The signals , and are unbounded for all bounded inputs
Option (A), If 
bounded input
Say 
unit step function, 
False, statement.
Option (B), As check above for bounded i/p of unit step function, 
are unbounded.
Hence, True statement.
Option (C), if u(t) is bounded, then all poles of 
will lies in LHS of 
-plane.
Thus, all poles of 
will also lies in LHS of s-plane.
For bounded, 
always bounded.
False, statement.
option (D), As check above, if always bounded,
then also always bounded.
Hence, option (b) is correct.