A second-order linear time-invariant system is described by the following state equations [rmdrmdt] x1(t) + 2x1(t) = 3u(t) [rmdrmdt] 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

This question belongs to Electronics And Communications Engineering Control Systems

Control Systems

A second-order linear time-invariant system is described by the following state equations
\[\frac{{\rm{d}}}{{{\rm{dt}}}}\] x₁(t) + 2x₁(t) = 3u(t)
\[\frac{{\rm{d}}}{{{\rm{dt}}}}\] 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) controllable but not observable B) observable but not controllable C) both controllable and observable D) neither controllable nor observable

Answer & Solution

Correct Answer: Option A

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