function sync
a=4,b=1,c=1,k=12,d=4.5,f=21.9,z=1,beta=0;
E=[eye(4),zeros(4,2)];
A=[-a a 0 0 0 0;0 0 0 1 0 1;0 0 0 0 1 0;0 -c 0 0 0 0];
C=[1 1 2 0 0 0;3 2 1 2 3 3;2 0 0 1 1 0;2 3 2 2 3 3;1 2 0 0 0 0];
H = [eye(3),zeros(3)]
r1=rank(C)
[m,n] = size(E)%(m \leq n)
n=rank([E;C])
[U,D,V]= svd(C)
D1=D(1:5,1:5)
Q = (V.')*([inv(D1) zeros(5,1);zeros(1,5) eye(n-r1)])
E2 = E*Q*[zeros(r1,(n-r1));eye(n-r1)]
[u,D2,v]=svd(E2)
D22 =0.7518
Ro = [zeros(m+r1-n,1),eye(m+r1-n);v*D22,zeros(1,m+r1-n)]*u
R = Q*[zeros(n-m,m);Ro]
E_cap = R*E
e_cap =[E_cap, zeros(6);zeros(6) ,eye(6)]
A_cap = R*A
%calculating LMI
setlmis([])
P = lmivar(1,[size(A_cap,1) 1]);
K_cap = lmivar(2,[6 5]);
lmiterm([1 1 1 P],1,A_cap,'s');
lmiterm([1 1 1 K_cap],-1,C,'s');
lmiterm([1 1 1 0],z*f^2*H'*H);
lmiterm([1 1 1 0],beta*eye(6));
lmiterm([1 1 2 P],1,R);
lmiterm([1 2 2 0],-z*eye(4));
LMISYS = getlmis;
[tmin,Psol]=feasp(LMISYS);
[tmin,Ksol]=feasp(LMISYS);
P = dec2mat(LMISYS,Psol,P)
K_cap = dec2mat(LMISYS,Ksol,K_cap)
K = inv(P)*K_cap
N = A_cap-K*C
M = eye(6)*pinv(C)-E_cap*pinv(C)
L =K+N*M
tspan = 0:0.1:60;
x0 = [1;1;1;1;1;4.5;-1;-1;-1;-1;-1;-1];
opt = odeset('Mass',e_cap,'RelTol',1e-8,'AbsTol',1e-8);
[t,x] = ode15s(@odesync,tspan,x0,opt);
function dxdt = odesync(t,x)
F= [0;k*x(1)*sin(x(3));-x(1)*x(2);0]
F_cap= [0;k*x(7)*sin(x(9));-x(7)*x(8);0]
y = C*[x(1);x(2);x(3);x(4);x(5);x(6)]
x_cap = [x(7);x(8);x(9);x(10);x(11);x(12)]+M*y
dxdt = A_cap*[x(1);x(2);x(3);x(4);x(5);x(6)] + R*F;
N*[x(7);x(8);x(9);x(10);x(11);x(12)]+L*y + R*F_cap
end
end
My errors are:-
Error using odearguments (line 95)
SYNC/ODESYNC returns a vector of length 6, but the length of initial conditions vector
is 12. The vector returned by SYNC/ODESYNC and the initial conditions vector must have
the same number of elements.
Error in ode15s (line 150)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in sync (line 43)
[t,x] = ode15s(@odesync,tspan,x0,opt);
