Please Solve error occurring while solving differential equation with ode15s

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);

Answer 1

[Wan Ji]

Just rewrite

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

to

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];

Then it works, but you should still check some other errors

[Meenakshi Tripathi]

Thank you so much!!! It worked.

[Meenakshi Tripathi]

Warning: Failure at t=2.292185e-04. Unable to meet integration tolerances without

reducing the step size below the smallest value allowed (4.336809e-19) at time t.

> In ode15s (line 668)

In sync (line 43)

>>program got run but getting this error now. Please tell me what is the meaning of this error?

[Wan Ji]

@Meenakshi Tripathi That means the ode15s can't reach a converged solution, you may check your odefun or set the options to see how each integration step works