Fall 2001 16.3116-8 Now very simple to form 10 l1 A-LC a201 l2|100 -a300 l3 Z110 l201 l300 The closed-loop poles of the estimator are at the roots of det(I-A+LC)=s32+(a1+4)2+(a2+l2)s+(a3+l3)=0 So we have the freedom to place the closed-loop poles as desired Task greatly simplified by the selection of the state-space model used for the design/analysisFall 2001 16.31 16—8 • Now very simple to form A − LC =   −a1 1 0 −a2 0 1 −a3 0 0   −   l1 l2 l3  £ 1 0 0 ¤ =   −a1 − l1 1 0 −a2 − l2 0 1 −a3 − l3 0 0   — The closed-loop poles of the estimator are at the roots of det(sI − A + LC) = s3 + (a1 + l1)s2 + (a2 + l2)s + (a3 + l3)=0 • So we have the freedom to place the closed-loop poles as desired. — Task greatly simplified by the selection of the state-space model used for the design/analysis