convertquadratics.m

国外专家做的求解LMI鲁棒控制的工具箱,可以相对高效的解决LMI问题

function [Fconv,no_changed] = convertquadratics(F)
%CONVERTQUADRATICS Internal function to extract quadratic constraints

% Author Johan L鰂berg
% $Id: convertquadratics.m,v 1.7 2004/12/21 13:22:29 johanl Exp $

% ******************************
% LINEAR?
% ******************************

%[nlmi,neq]=size(F);
%itslinear    = 1;
%itssigmonial = 0;

itslinear = islinear(F);
if itslinear
    Fconv = F;
    no_changed = 0;
    return
end

itssigmonial = issigmonial(F);
if itssigmonial
    Fconv = F;
    no_changed = 0;
    return
end

Fconv = lmi;
no_changed = 0;
for i = 1:1:length(F)
    if is(F(i),'element-wise') & ~is(F(i),'linear') & ~is(F(i),'sigmonial')
        % f-c'*x-x'*Q*x>0
        [Q,c,f,x,info] = quaddecomp(sdpvar(F(i)));
        %        [G,info]=nonlineartocone(getconstraint(F(i)));
        if info==0
            % Yes, quadratic, but convex?
            % Change sign definitions
            Q = -Q;
            c = -c;
            f = -f;
            % Semi-definite case when only part of x in Q
            % Occurs, e.g, in constraints like y'*Q*y < t
            used = find(any(Q));Qred=Q(:,used);Qred = Qred(used,:);xred = x(used);
            [R,p]=chol(Qred);
            if p==0
                % Write as second order cone
                d = -c'*x-f;
                if isa(d,'double') & d==1
                    Fconv=Fconv + lmi(cone([2*R*xred],1+d));
                else
                    Fconv=Fconv + lmi(cone([2*R*xred;1-d],1+d));
                end
                no_changed = no_changed + 1;
            else
                Fconv = Fconv + F(i);
            end
        else
            Fconv = Fconv + F(i);
        end
    else
        Fconv = Fconv + F(i);
    end
end