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ECE · Q158

Control Systems

Engineering and GATE · ECE · question 158

Q158

A second-order linear time-invariant system is described by the following state equations \[ d dt\] x1(t) + 2x1(t) = 3u(t) \[ d dt\] x2(t) + x2(t) = u(t) where x1(t) and x2(t) are the two state variables and u(t) denotes the input. If the output c(t) = x1(t) , then the system is

A second-order linear time-invariant system is described by the following state equations
x1(t) + 2x1(t) = 3u(t)
x2(t) + x2(t) = u(t)
where x1(t) and x2(t) are the two state variables and u(t) denotes the input. If the output c(t) = x1(t) , then the system is
A.
controllable but not observable
Answer
B.
observable but not controllable
C.
both controllable and observable
D.
neither controllable nor observable

Answer: Option A

Solution

Answer: Option A
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