Fall 2001 16.3116-3 X() SYSTEM A B.c y() u(七 DBSERVER A,8.C 文( Analysis of this case i(t)= Ac+Bu( i(t)=A.c+Bu(t) Define the estimation error (t)=a(t-i(t) Now want c(t)=0Vt. But is this realistic?) Subtract to get dt x-)=Ax-)→(t)=A which has the solution (t) At Gives the estimation error in terms of the initial errorFall 2001 16.31 16—3 • Analysis of this case: x˙(t) = Ax + Bu(t) ˙ xˆ(t) = Axˆ + Bu(t) • Define the estimation error x˜(t) = x(t) − xˆ(t). Now want ˜x(t)=0 ∀ t. (But is this realistic?) • Subtract to get: d dt(x − xˆ) = A(x − xˆ) ⇒ x˜˙(t) = Ax˜ which has the solution x˜(t) = eAtx˜(0) — Gives the estimation error in terms of the initial error