% Script Tab12_6.m; 747 altitude/airspeed SAS; feedback gains, closed-
% loop eigenvalues, and worst initial conditions; x=[u,w,q,theta,h,
% delta t]'; u=[delta e,delta tc]; units ft, sec, crad.
%
F=[-.003 .039 0 -.322 0 1; -.065 -.319 7.74 0 0 -.04; .0201 -.101 ...
-.429 0 0 .598; 0 0 1 0 0 0; 0 -1 0 7.74 0 0; 0 0 0 0 0 -.25];
G=[.01 -.18 -1.16 0 0 0; 0 0 0 0 0 .25]'; H=[1 0 0 0 0 0; 0 0 0 0 1 0];
A=.25*diag([1 .01]); B=eye(2); L=zeros(2); [k,S,ev]=lqr(F,G,H'*A*H,B);
[v,d]=eig(S); [J,l]=max(diag(d)); x0=v(:,l)/norm(v(:,l));
k, ev, x0'
