i am trying to solve a nonholonomic system against a given controller using ode solver but cann't get the right results.

the controller is designed using model decomposition.the system has six states.

the mathematics for the controller is sound and all states should go to zero against a given initial condition.for different initial condition the sign of d5 and d6 is altered in the controllers to get convergence.

I have tried all possible scenarios but can't get the convergence.i also need to know if the variable 't' {cos(2*pi*t) and sin(2*pi*t)} in my controller has any thing to do with the problem.

the complete code is as follow

function dx=lbracket(t,x)
 dx = zeros(6,1);
 % define state variables
 T=0.5;
 x1 = x(1);
 x2 = x(2);
 x3 = x(3);
 x4 = x(4);
 x5 = x(5);
 x6 = x(6);
v1=-x1-x2*x3-x4*x5;
v2=-x2;
v3=-x4;
v4=-x6;
v5=x3;
v6=x5;

   d5=3.54491*sign(v5)*sqrt(abs(v5)/T);
   d6=3.54491*sign(v6)*sqrt(abs(v6)/T);

   u1=v1+d5*sin((2*pi*t)/T)-d6*cos((2*pi*t)/T);
   u2=v2-d5*cos((2*pi*t)/T);
   u3=v3+d6*cos((2*pi*t)/T);
   u4=v4;
  % 
  % 
   dx(1)     =  u1;
   dx(2)     =  u2;
   dx(3)     =  x(2)*u1;
   dx(4)     =  u3;
   dx(5)     =  x(4)*u1;
   dx(6)     =  u4;
   end

% function lbracket called in another m-file

Tspan = [0 50]; 

IC = [2 2 2 2 2 2];
options = odeset('RelTol',1e-2,'AbsTol',[1e-2 1e-2 1e-2 1e-2 1e-2 1e-2]);
[T,Y] = ode45(@lbracket, Tspan,IC,options);

x1  =   Y(:,1);
x2  =   Y(:,2);
x3  =   Y(:,3);
x4  =   Y(:,4);
x5  =   Y(:,5);
x6  =   Y(:,6);

figure()
plot(T,x1,T,x2,T,x3,T,x4,T,x5,T,x6,'linewidth',2)
legend('x1','x2','x3','x4','x5','x6',6);
xlabel('t(s)')
ylabel('x_1,x_2,x_3,x_4,x_5,x_6')
grid on