function ps81(a)
if nargin<1, a=1; end
s=tf('s');
p=ss(0,[1 0 1],[a;1],[0 0 1;0 1 0]);
[K1,~,GAM1]=hinfsyn(p,1,1);   % numerical solution
if a>0,
    K=-a;
    GAM=a;
else
    r=roots([1, -2-a^2, 1-2*a^2, -a^2]);
    r=max(r(r==real(r)));
    P=sqrt(r*(r-a^2));
    K=-r/(P+a);
    GAM=sqrt(r);;
end
CL=lft(p,K);
GAM2=norm(CL,Inf);
K0=squeeze(freqresp(K1,[0]));
fprintf('-K:    analytical %f, numerical %f\n',-K,-K0)
fprintf('GAMMA: analytical %f, numerical %f, achieved %f\n', ...
    GAM,GAM1,GAM2)