gre.m

一个时滞系统的工具箱

function [P,D1,D2]=gre(A0,A1,B,delay,M,N)
%GRE solves the generalized Ricatti equations corresponding to 
%  the linear quadratic regulator problem for systems with delays. 
%  For the system x'= A0*x + A1*y(-delay) + B*u , this function can be
%  used for calculating the coefficients of the optimal control    
%
%   u=-inv(N)B'Px+integral(-delay,0,D0*exp(D1)*D2*y(s))ds
%   
%   INPUT :		
%	A0,A1,B  - System coefficient
%  	delay - State delay
%  	M     - Positive symmetric nxn state weighting matrix(n is the system order)
%  	N     - Positive symmetric input weighting matrix
%  OUTPUT :
%     P     - Solution of P*A0+A0'*P+M=P*K*P 
%     K=B*inv(N)*B' 
%  	D1=-(P*K-A0')
%  	D2=exp(D1*delay)*P*A1
%  

misdefinite=isdef(M);
nisdefinite=isdef(N);
if((length(misdefinite)==17) & (length(nisdefinite)==17))
   if((sum(misdefinite=='positive definite')==17)&(sum(nisdefinite=='positive definite')==17))
      [gain P eigenvalue]=lqr(A0,B,M,N);		
      K=B*inv(N)*(B');      
      D1=-(P*K-A0');
      D2=expm(D1*delay)*P*A1;
   else
      disp('You must input positive matrix M and N'); 
   end 
else
   disp('You must input positive matrix M and N'); 
end