Fall 2001 Examples 6.3112-5 With Model #2: 30 CA 60 [ B AB I rank Mo= l and rank Mc=2 So this model of the system is controllable, but not observable 2 With Model #3: C CA 6-2 C B AB 00 rank Mo=2 and rank Mc=1 So this model of the system is observable, but not controllable Note that controllability /observability are not intrinsic properties of a system. Whether the model has them or not depends on the representation that you choose But they indicate that something else more fundamental is wrong˙ ˙ Fall 2001 Examples 16.31 12—5   − ∙ 2 0 With Model # 2: x¯ =  x¯ + 1 2 ¸ u 0 −1 £ y = 3 0 ¤ x¯ ∙ ∙ C 3 0 M0 = CA ¸ = −6 0 ¸ ∙ Mc = £ B AB ¤ = 2 −4 1 −1 ¸ — rank M0 = 1 and rank Mc = 2 — So this model of the system is controllable, but not observable.   − ∙ 2 0 With Model # 3: x¯ =  x¯ + 0 2 ¸ u 0 −1 £ y = 3 2 ¤ x¯ ∙ ∙ C 3 2 M0 = CA ¸ = −6 −2 ¸ Mc = £ B AB ¤ = ∙ 2 0 −4 0 ¸ — rank M0 = 2 and rank Mc = 1 — So this model of the system is observable, but not controllable. • Note that controllability/observability are not intrinsic properties of a system. Whether the model has them or not depends on the representation that you choose. — But they indicate that something else more fundamental is wrong