1. Consider a single-input, single-output third-order system described by 1 0 dx dt b0 1 x...

  

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1. Consider a single-input, single-output third-order system described by 1 0 dx dt b0 1 x + C 00 U y=[e 0 0]a, e>0 Obtain the transfer function from u to y. Examine the controllability and observability of this system. Show that a pole-zero cancellation in the transfer function takes place if this system is to lose either controllability or observability. Your answer to the last question should be based on the controllability matrix or the observability matrix. Recall that a square matrix is not full rank if and only if its determinant is zero. 1. Consider a single-input, single-output third-order system described by 1 0 dx dt b0 1 x + C 00 U y=[e 0 0]a, e>0 Obtain the transfer function from u to y. Examine the controllability and observability of this system. Show that a pole-zero cancellation in the transfer function takes place if this system is to lose either controllability or observability. Your answer to the last question should be based on the controllability matrix or the observability matrix. Recall that a square matrix is not full rank if and only if its determinant is zero.