### 1. The following LTI system is given: [ begin{array}{l} dot{x}(t)=left[begin{array}{ll} 3 & -2 \ 4 & -3 end{array}right] x(t)+left[begin{array}{c} 1 \ -1 end{array}right] u(t) \ y(t)=left[begin{array}{ll} 1 & 0 end{array}right] x(t) end{array} ] (a) Design an observer such that the error dynamics have eigenvalues at ( -4 ) and ( -2 ).

1. The following LTI system is given: [ begin{array}{l} dot{x}(t)=left[begin{array}{ll} 3 & -2 \ 4 & -3 end{array}right] x(t)+left[begin{array}{c} 1 \ -1 end{array}right] u(t) \ y(t)=left[begin{array}{ll} 1 & 0 end{array}right] x(t) end{array} ] (a) Design an observer such that the error dynamics have eigenvalues at ( -4 ) and ( -2 ).