format compact
format short e
delete sat5.out
echo on
diary sat5.out
% MAE 280 B - Linear Control Design
% Mauricio de Oliveira
%
% LMI Stabilizing Control
%

m = 100;               % 100 kg
r = 300E3;             % 300 km
R = 6.37E6;            % 6.37 10^3 km
G = 6.673E-11;         % 6.673 N m^2/kg^2
M = 5.98E24;           % 5.98 10^24 kg
k = G * M;             % gravitational force constant
w = sqrt(k/((R+r)^3)); % angular velocity (rad/s)
v = w * (R + r);       % "ground" velocity (m/s)

% linearized system matrices
A = [0 0 1 0; 0 0 0 1; 3*w^2 0 0 2*(r+R)*w; 0 0 -2*w/(r+R) 0];
Bu = [0 0; 0 0; 1/m 0; 0 1/(m*r)];

% scale
T = diag([1 r 1 r])

% similarity transformation
At = T * A / T
But = T * Bu

% stabilizing state feedback control (using u2 only)
n = size(At,1);
m = 1;

% declare variables
X = sdpvar(n,n,'symmetric');
L = sdpvar(m,n);

% declare LMIs
LMI1 = At*X+X*At'+But(:,2)*L+L'*But(:,2)';
LMI2 = X;

LMI = set(LMI1 < 0) + set(LMI2 > 0);
options = sdpsettings('solver','sedumi');
solution =solvesdp(LMI,[],options)

eig(double(LMI1))
eig(double(LMI2))

% Construct K and check closed loop stability
K = double(L) / double(X)
Acl = At + But(:,2)*K;
eig(Acl)

% stabilizing state feedback control (using u1 and u2)
n = size(At,1);
m = 2;

% declare variables
X = sdpvar(n,n,'symmetric');
L = sdpvar(m,n);

% declare LMIs
LMI1 = At*X+X*At'+But*L+L'*But';
LMI2 = X;

LMI = set(LMI1 < 0) + set(LMI2 > 0);
options = sdpsettings('solver','sedumi');
solution =solvesdp(LMI,[],options)

eig(double(LMI1))
eig(double(LMI2))

% Construct K and check closed loop stability
K = double(L) / double(X)
Acl = At + But*K;
eig(Acl)

diary off
echo off