tf2ss.m

数字通信第四版原书的例程

function [a,b,c,d] = tf2ss(num, den)
%TF2SS	Transfer function to state-space conversion.
%	[A,B,C,D] = TF2SS(NUM,DEN)  calculates the state-space 
%	representation:
%		.
%		x = Ax + Bu
%		y = Cx + Du
%
%	of the system:
%		        NUM(s) 
%		H(s) = --------
%		        DEN(s)
%
%	from a single input.  Vector DEN must contain the coefficients of
%	the denominator in descending powers of s.  Matrix NUM must 
%	contain the numerator coefficients with as many rows as there are
%	outputs y.  The A,B,C,D matrices are returned in controller 
%	canonical form.  This calculation also works for discrete systems.
%	To avoid confusion when using this function with discrete systems,
%	always use a numerator polynomial that has been padded with zeros
%	to make it the same length as the denominator.  See the User's
%	guide for more details.
%
%	See also: SS2TF.

% 	J.N. Little 3-24-85
%	Copyright (c) 1986-93 by the MathWorks, Inc.
%	Latest revision 4-29-89 JNL

[mnum,nnum] = size(num);
[mden,n] = size(den);
% Check for null systems
if  (n == 0 & nnum == 0), a=[]; b=[]; c=[]; d=[]; return, end

% Strip leading zeros from denominator
inz = find(den ~= 0);
den = den(inz(1):n);
[mden,n] = size(den);

% Check for proper numerator
if nnum > n
	% Try to strip leading zeros to make proper
	if (all(all(num(:,1:(nnum-n)) == 0)))
		num = num(:,(nnum-n+1):nnum);
		[mnum,nnum] = size(num);
	else
		error('Denominator must be higher or equal order than numerator.');
	end
end

% Pad numerator with leading zeros, to make it have the same number of
% columns as the denominator, and normalize it to den(1)
num = [zeros(mnum,n-nnum) num]./den(1);

% Do the D-matrix first
if length(num)
	d = num(:,1);
else
	d = [];
end

% Handle special constant case:
if n == 1
	a = [];
	b = [];
	c = [];
	return
end

% Now do the rest, starting by normalizing den to den(1),
den = den(2:n) ./ den(1);
a = [-den; eye(n-2,n-1)];
b = eye(n-1,1);
if mnum > 0
	c = num(:,2:n) - num(:,1) * den;
else
	c = [];
end