Consider the system x(k+1) =Gx(k) + Hx(k) where ![G = \left[\begin{array}{ccc}0&1\\-0.16&-1\end{array}\right]](https://tex.z-dn.net/?f=G+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B1%5C%5C-0.16%26amp%3B-1%5Cend%7Barray%7D%5Cright%5D "G = \left[\begin{array}{ccc}0&1\\-0.16&-1\end{array}\right]")
, ![H= \left[\begin{array}{ccc}0\\1\\\end{array}\right]](https://tex.z-dn.net/?f=H%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C1%5C%5C%5Cend%7Barray%7D%5Cright%5D "H= \left[\begin{array}{ccc}0\\1\\\end{array}\right]")
determine a suitable state feedback gain matrix k such that the system will have the closed loop poles at z = 0.5 + j0.5, z = 0.5 - j0.5
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