Consider the following LTI system: $$ x(k+1)= \begin{bmatrix} 0 & 1 \\ 1 & 0 \\ \end{bmatrix} x(k) + \begin{bmatrix} 0 \\ 1 \\ \end{bmatrix} u(k) \quad {and} \quad y(k) = \begin{bmatrix} 0 & 1\\ \end{bmatrix} \\ $$ Design a state observer so that the state estimation error $$ e(k) = x(k) - \hat{x}(k) = 0 \text{ for k } \geq \text{ 2} $$
How do you determine the L matrix from this? I have done problems where they provide poles placement. But this problem is different where it asks for zero error when k>=2