Documentation of thc2thd

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Function Synopsis

thd=thc2thd(thc,T)

Help text

THC2THD  Converts a continuous time model to discrete time.
   THD = THC2THD(THC,T)

   THC: The continuous time model, specified in THETA format
           (See also THETA).

   T: The sampling interval
   THD: The discrete time model, in THETA format

   Note that the covariance matrix is not translated to discrete time
   for input-output type models

   See also THD2THC.

Cross-Reference Information

Listing of function thc2thd

function thd=thc2thd(thc,T)

%   L. Ljung 10-2-90, 94-08-27
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.4 $  $Date: 1997/12/02 03:44:39 $

if nargin < 2
   disp('Usage: THD = THC2THD(THC,T)')
   return
end

Told=gett(thc);
if Told>0,error('This model is already denoted as discrete-time!'),end
if T<0,error('The sampling interval must be positive!'),end
lamscale=abs(Told)/T;
[nrth,ncth]=size(thc);[p,covp,lam]=th2par(thc);nnd=length(p);nu=thc(1,3);
if isthss(thc)
        rarg=thc(1,6);ny=thc(1,4);
        thd=thc; thd(1,2)=T;
        thd(4+nnd+rarg:nrth,1:ny)=lamscale*lam;
        thd(1:2,1)=lamscale^ny*thc(1:2,1);
        return
end
if nrth>3+nnd,delays=thc(nrth,1:nu);else delays=zeros(1,nu);end

nnk=[round(delays/T) 0];
[a,b,c,d,k]=th2ss(thc);nu=thc(1,3);
[m,n] = size(a);
[m,nb] = size(b);
[m,nk] = size(k);

s = expm([[a b k]*T; zeros(nb+nk,n+nb+nk)]);
a = s(1:n,1:n);
bk = s(1:n,n+1:n+nb+nk);
dk = [d 1];

den = poly(a);

[mc,nc] = size(c);
for iu=1:nu+1
    b1 = bk(:,iu);
    d1 = dk(:,iu);
    num1 = poly(a-b1*c) + (d1 - 1) * den;
    num(iu,1:length(num1)+nnk(iu))=[zeros(1,nnk(iu)) num1];
end

thd=poly2th(den,num(1:nu,:),num(nu+1,:),1,ones(nu,1),lamscale*lam,T);
thd(2,1)=thc(2,1)*lamscale;