function [Y,degY] = rypol(F,Hb,Hc,mes)

%  to find polynomial matrix from state-space condition  
%         [Y0 Y1...]*observ(Hb,F) = Hc
%
%  Y  ... pol.matrix Y(z)=Y0+Y1*z+Y2*z^{2}+... 
%  degY . degree of Y
%  F  ... state-feedback matrix      
%  Hb ... input matrix 
%  Hc ... input matrix                
%  mes (=0,1,2)...message and interrupt level 
%                                                         
%  Call: [Y,degY]=rypol(F,Hb,Hc,mes)

to = 1e-6;

[rHb,cHb] = size(Hb);
[rHc,cHc] = size(Hc);
[rF,cF] = size(F);
if (rF ~= cF)|(cHb ~= cHc)|(cF ~= cHb)
  error('contr: F,Hb,Hc not compatible with assumptions')
end

observ = Hb; for i = 1:cHb-1, observ = [Hb; observ*F]; end
normS = norm([observ; Hc]',inf);

ub = rHb*cHb;
sel=1:ub;
Y=zeros(rHc,ub); degY=cHb-1;
unsolvable = 0;

for l=1:rHc
  if unsolvable == 1
     disp('....................................................')
     disp('no solution: A,B,C violate the span condition ')
     disp('....................................................')
     Y = []; degY = [];
     return
  end 
  i=1;   
  unsolvable = 1;
  while i<=ub
    b=observ(sel(1,i),:);  B=[Hc(l,:); observ(sel(1,1:i-1),:)];
    c=b/B;
    err=b-c*B;
    if norm(err,2) <= to*normS
      % check row Hc(l) for independence       
      if abs(c(1,1)) > 1e-14
	c = [c  -1]; c = -c/c(1,1);
        for chknan=1:i 
          if c(1,chknan)==NaN, c(1,chknan)=0;  end 
        end
	Y(l,sel(1,1:i)) = c(1,2:i+1);
        unsolvable = 0;
 	break
      end
      % select the dependent rows of observability matrix
      ii = i;  idel = sel(1,i);
      while ii <= ub
	if sel(1,ii) == idel
	  sel = [sel(1,1:ii-1) sel(1,ii+1:ub)];
	  ub = ub - 1; 
	  idel = idel + rHb;
	end
	ii = ii + 1;
      end
      i = i - 1;
    end
    i = i + 1;
  end
end

[Y,degY]=polcl(Y,degY);