% demonstrate findPISaddPIS;		% Add the PosInvSet directory to MATLAB's pathclear;if exist('qhull')==3    clc;    fprintf(1,'\t\tInvariant Set for MOD2 (findPIS) \n\n');    order=2;    dsistest    fprintf(1,'paused\n');    pause    clc;    fprintf(1,'\t\tInvariant Set for a 3rd-order modulator (findPIS) \n\n');    order=3;    dsistestelse    clc;    fprintf(1,'\t\tInvariant Set for MOD2 (find2dPIS) \n\n');    mod = mod2;    ABCD = mod.ABCD; [A B C D] = partitionABCD(ABCD);    order=2;    figure(1);    echo on;    u = 1/pi;    t = cputime;    s = find2dPIS(u,ABCD,1)    t = cputime-t    echo off;    N=10000; skip=100;    [junk x] = simulateDSM(u(ones(1,N+skip)),ABCD,2);    x = x(:,1+skip:N+skip);    nv = size(s,2);    [splus, eplus, sminus, eminus] = dssplit2d(u,ABCD,s);    Buv = B*[u;1];    s1 = A*splus + Buv(:,ones(1,size(splus,2)));            Buv = B*[u;-1];    s2 = A*sminus + Buv(:,ones(1,size(sminus,2)));           ns = [s1 s2];                            out = outconvex2d(ns,s);    figure(2);    clf; hold on; grid;    dotplot(x,'k.');    polyplot(s,'b');    polyplot(s1,'m');    polyplot(s2,'c');    outi = logical(sign(out));    dotplot(ns(:,outi),'rs');    str = sprintf('Final Object: %d image vertices outside', sum(outi));    title(str);    figure(gcf);    fprintf(1,'%d points from the %d simulated states are outside.\n', sum(outconvex2d(x,s)),N);    fprintf(1,'%d image points are outside.\n', sum(out));             fprintf(1,'The returned polygon has %d vertices.\n', size(s,2));end