Question about the solutions (Dual infeasible, primal improving direction found.)

[So Watt]

Hello there, I'm new to YALMIP and I wanted to ask you about the solutions I obtained:

n = 2;
gamma=1.6817;
Q= [1.0841    0.1752  ;  0.1752    1.0841];
%%%% Controller variables
Ac=0;
Bc=1;
Cc=sdpvar(1,1);
Dc=sdpvar(1,1);
%%%% Model
delta = 1;
A=0;Bw=[-delta 0];Bu =1;
Ce=[1;0]; Dew=zeros(2);Deu= [0;1];
Cy =1;Dyw=[0 1];Dyu=0;

Af = [A+Bu*Dc*Cy Bu*Cc;Bc*Cy Ac];
Bf = [Bw+Bu*Dc*Dyw;Bc*Dyw];
Cf= [Ce+Deu*Dc*Cy Deu*Cc];
Df=[Dew+Deu*Dc*Dyw];


% LMI
% LBR = [Af>=0];
LBR = [Af'*Q+Q*Af Q*Bf Cf';Bf'*Q -gamma*eye(2) Df';Cf Df -gamma*eye(2)]<=0;
%% solving
Sol= optimize(LBR);

lam1 = value(Dc)
lam2 = value(Cc)

I'm solving to find Cc and Dc (which should have the same sign) but I'm getting this message :

Dual infeasible, primal improving direction found.
iter seconds  |Ax|    [Ay]_+     |x|       |y|
 14      1.5   1.2e-10   2.1e-10   6.0e+00   2.0e-10
lam1 =

  -1.9639e-10


lam2 =

   2.7153e-11

Is something wrong with my formulation or the solver? or my problem is infeasible?

Thank you

[Johan Löfberg]

It's infeasible. Smallest possible gamma is 6.27

sdpvar gamma

LBR = [Af'*Q+Q*Af Q*Bf Cf';Bf'*Q -gamma*eye(2) Df';Cf Df -gamma*eye(2)]<=0;

%% solving

Sol = optimize(LBR,gamma)

[So Watt]

Thank you for the response, It really helps a lot,

If my gamma is only constrained with (Gamma>sqrt(2)),

does that mean that my problem is feasible ? (by choosing gamma in the appropriate range)

[Johan Löfberg]

6.27 is larger than sqrt(2) last time I checked

[So Watt]

Thank you, Just checking,

The constraint on gamma is obtained from another LMI, I just wanted to double check