The state equation of a second-order linear system is given by, [mathop xlimits^ ( t ) = Ax( t ),x( 0 ) = x_0] For [x_0 = [ l 1 - 1 ],x( t ) = [ l e^ - t - e^ - t ]] and for [x_0 = [ l 0 1 ],x( t ) = [ l e^ - t - e^ - 2t - e^ - t + e^ - 2t ].] When [x_0 = [ l 3 5 ],x( t )] is

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Control Systems

The state equation of a second-order linear system is given by, \[\mathop x\limits^ \cdot \left( t \right) = Ax\left( t \right),\,x\left( 0 \right) = {x_0}\]
For \[{x_0} = \left[ \begin{array}{l} 1\\ - 1 \end{array} \right],\,x\left( t \right) = \left[ \begin{array}{l} {e^{ - t}}\\ - {e^{ - t}} \end{array} \right]\] and for \[{x_0} = \left[ \begin{array}{l} 0\\ 1 \end{array} \right],\,x\left( t \right) = \left[ \begin{array}{l} {e^{ - t}} - {e^{ - 2t}}\\ - {e^{ - t}} + {e^{ - 2t}} \end{array} \right].\]
When \[{x_0} = \left[ \begin{array}{l} 3\\ 5 \end{array} \right],\,x\left( t \right)\] is

A) \[\left[ \begin{array}{l} - 8{e^{ - t}} + 11{e^{ - 2t}}\\ 8{e^{ - t}} - 22{e^{ - 2t}} \end{array} \right]\] B) \[\left[ \begin{array}{l} 11{e^{ - t}} - 8{e^{ - 2t}}\\ - 11{e^{ - t}} + 16{e^{ - 2t}} \end{array} \right]\] C) \[\left[ \begin{array}{l} 3{e^{ - t}} - 5{e^{ - 2t}}\\ - 3{e^{ - t}} + 10{e^{ - 2t}} \end{array} \right]\] D) \[\left[ \begin{array}{l} - 5{e^{ - t}} + 6{e^{ - 2t}}\\ - 5{e^{ - t}} + 6{e^{ - 2t}} \end{array} \right]\]

Answer & Solution

Correct Answer: Option B

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