contfracfeval.m

国外人编写的一个分数阶系统的控制工具箱

function out = contfracfeval (a, b, n, x)

% out = contfraceval (a, b, n, x)
% This function evaluates at point x
% the continued fraction expansion of a function
% given by a = [a0 a1 a2 a3...]
% and b = [b0 b1 b2 b3...]
% where b0 must be 0.
% The continued fraction is
%               b1
% a0 + ---------------------
%               b2 * x
%      a1 + ---------------
%                  b3 * x
%           a2 + ---------
%           
%                a3 + ...
% Variable out is reckoned for the several values of n
% according to the recursive formulas
% out(n) = P(n) / Q(n)
% P(0) = a0
% Q(0) = 1
% P(-1) = 1
% Q(-1) = 0
% P(n) = a(n) * P(n-1) + b(n) * P(n-2)
% Q(n) = a(n) * Q(n-1) + b(n) * Q(n-2)
% which are more efficient than direct evaluation
% and allow for a progressive reckoning of approximations that keep on improving.
% Of course max(n) should not be greater than length(a)-1 or length(b)-1.
% For obtaining solely the best possible value of the series make n=min[length(a) length(b)]-1.

b = b .* [0 1 x*ones(1,length(b)-2)];
out = contfraceval (a, b, n);