Which solver is good Lyapunov stability problem?

[Samrat Dutta]

I'm using LMILab solver for Lyapunov stability LMI but getting an objective value NAN. Which solver is the best for this kind of problem?

A=data.A;

B=data.B;

LMI1=[];

LMI2=[];

LMI3=[];

LMI4=[];

X=sdpvar(ni);

for i=1:nr

 Y{i}=sdpvar(nu,ni);

 Q{i}=sdpvar(ni);

end

for r=1:nr

    Ar=A(:,:,r);

    Br=B(:,:,r);

   

    LMI1= LMI1 + setLMI1(Ar,Br,Q{r},Y{r}, X,nr);

   

  

end

for i=1:nr

    for j=i:nr

        Ai=A(:,:,i);

        Aj=A(:,:,j);

        Bi=B(:,:,i);

        Bj=B(:,:,j);

        

       

   

        LMI2= LMI2 + setLMI2(Ai,Aj,Bi,Bj, Q{i},Q{j},Y{i}, Y{j}, X);

    end  

    

end

for r=1:nr

 LMI3 = LMI3 + set(Q{r}>0);

%  LMI4 = LMI4 +set(Q{r}<500*eye(ni));

end

LMI5=set(X>=0);

 ineqs = LMI1 + LMI2 + LMI3 + LMI4 + LMI5;

 

 gamma2=0;

 for r=1:nr

    gamma2=gamma2+norm(double(Y{r})*inv(double(Q{r})));

 end

 

 opts=sdpsettings;

opts.solver='lmilab';

opts = sdpsettings(opts,'verbos',0);

%  warning('off','YALMIP:strict') 

yalmipdiagnostics=solvesdp(ineqs,gamma2,opts);

[Johan Löfberg]

What is returned by solvesdp, i.e. yalmipdiagnostics

Note, SET is obsolete
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Set

and strict inequalities is not supported in practice
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Blog.Prepare-your-code

[Samrat Dutta]

Thank you very much for your reply. I'll make those changes. There are few things that I wanted to know

1) I'm using "LMILab" solver for Lyapunov stability problem but the answers are not as expected. The objective parameter value becomes infinity. Is the "LMILab" solver is OK for Lyapunov stability problem?

2) Is it ok that I'm minimizing the norm of a 'sdpvar' type?

[Johan Löfberg]

1. I guess you haven't read this
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Solvers.LMILAB

2. Yes, many norms are SDP/SOCP/LP representable

[Samrat Dutta]

yes, I missed it. Thanks!

I tried with sdpt3, but it's saying infeasible solution. Is it because a feasible solution doesn't really exist or may be some other solver can get a feasible solution? If later one is a possibility, can you kindly suggest a solver from your experience?

Thanks for your replies!  

[Johan Löfberg]

Could be infeasible, or simply extremly badly conditioned.

I use sedumi,sdpt3 and mosek