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Highlights from
synthesis

from synthesis by Evgeny Veremey
Solves SISO mean-square optimal control design problems: A(p)x = B(p)u + f(t)

[W1,W2,X,U]=alg2(A,B,N,T,mm)
function [W1,W2,X,U]=alg2(A,B,N,T,mm)
%The results of this program are:<x^2>,<u^2> and control W1/W2 
%calculated by the special algorithm 

% A(-s), B(-s);
A_=A(1)*((-1)^(length(A)+1))*poly(-1*roots(A));
if length(B)==1 B_=B;
else   B_=B(1)*((-1)^(length(B)+1))*poly(-1*roots(B));
end
% A(s)A(-s)+m^2*B(s)B(-s) ;
GG_=polsum(conv(A,A_),mm*conv(B,B_));
[G_,G]=polfac(GG_);
rootG_=roots(G_);
R=zeros(1,length(rootG_));
     for k=1:length(rootG_)
       q=rootG_(k);
       R=R-deconv(G_,[-1,q])*polyval(A,-1*q)*polyval(N,q)/polyval(T,q)/polyval(B,q)/polyval(polyder(G),-1*q);
     end;
    %U= W1(p) / W2(p) *x
    W1=deconv(polsum(conv(conv(T,A),R),(-1)*mm*conv(N,B_)),G_);
    W2=deconv(polsum(conv(conv(T,B),R),conv(N,A_)),G_);
    %<x^2>
    X=(norm(tf( W2,conv(T,G) ) ,2))^2*pi;
    %<u^2>
    U=(norm(tf( W1,conv(T,G) ),2))^2*pi;
    


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