Stability margins - continuous case

[Mariusz]

Hi,

I want to solve the following optimization problem

maximize Alpha
subject to:
             A * P + P * A '+ 2 * Alpha * P> 0
             P> 0
             Alpha> 0

My code:

function rP=LMIStabilityMargins(A)

%% set options for given solver
options=sdpsettings;
options.solver='sedumi';
options.showprogress=0;
options.verbose=0;
warning('off','YALMIP:strict');

%% size of matrix A
n=size(A,1);

%% clear yalmip state
yalmip('clear');

%% define variable matrices
P = sdpvar(n,n,'symmetric');
alpha_=sdpvar(1);

%% define inequalities LMI
LMIs = set([ ]);

%% use LMI variables
main_lmi = [P*A + A'*P + 2*alpha_*P];

LMIs = LMIs + set (alpha_ > 0, ['alpha_ > 0']);
LMIs = LMIs + set (P > 0, ['P > 0']);
LMIs = LMIs + set(main_lmi < 0,  'main_lmi < 0');          

%% solve it
res=solvesdp(LMIs,-alpha_ , options);

%%
if res.problem == 0  
    fprintf('=================================================================================\n');
    fprintf('Problem ...: %d\nInfo ......: %s\n', res.problem, res.info);
    if all(checkset(LMIs)>=0)
        fprintf('Everythings is all right :-)\n');
        fprintf('=================================================================================\n');
    else
        %disp(LMIs);
        %checkset(LMIs)
        fprintf('### Some LMIs are not feasible :-( ###\n');
        fprintf('=================================================================================\n');
    end
    rP = double(P);
else
   res.problem
   P=0;
end

When I want to solve, I have the following message:

Warning: Solver not applicable (sedumi)

ans =

     -4

Where is the problem in my code?

Regards,

[Johan Löfberg]

The problem is not linear so you don't have any solver to solve the problem

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Examples.DecayRate

and btw,
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Blog.Prepare-your-code

and
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.set