>极点配置定理一可配置的条件 Theorem5.2 The polesorigenvalues of theclosed-loop system by introducing the statefeedbackcontrol-can be placed arbitrarily iff theoriginalopen-loopsystemis completely controllable. 结论：线性定常闭环系统可通过状态反馈任意配置其全部极 点的充分必要条件是：原开环系统为完全能控的。 Proof:Sufficiency If the system(5.9)is completely controllable,then it is transformable into controllable canonical form(5.15)by a nonsingular transformation X=PX. (0)=A(0+(t) (5.15) y(t)=cX(t)
➢ 极点配置定理—可配置的条件 结论 ：线性定常闭环系统可通过状态反馈任意配置其全部极 点的充分必要条件是：原开环系统为完全能控的。 Proof: Sufficiency
0 1 0 0 0 0 0 1 0 0 where A=P-AP= b=Pb= 0 0 -dn-2 -41 c=cP=[bnbn-1.b2b] ☆ Since nonsingular state transformation does not change the transfer function,'so the transfer function of system(5.9)and (5.15)is 非奇异状态变换不改变 传递函数，特征多项式、 征根、能控性、能观 6,s+.+b5+b,性 (5.16) ”+a,s1+am-2+.+an-3+a
非奇异状态变换不改变 传递函数，特征多项式、 特征根、能控性、能观 性