initiald.m

一个时滞系统的工具箱

function [T,V]=initiald(tf,x0,initfun,a0,a1,b,c,d,delay,F,tol);
%INITIALD Initial condition response of continuous-time linear systems 
%	  with delays.
%	  INITIALD simulates the linear time-delay system
%       .
%       x(t) = A0*x(t)+A1*y(-delay)+int(-delay,0,F(s)*y(s))ds+B*u(t)
%		v(t) = C*x(t) + D*u(t)
%
%	  on the segment [0, tf], with the initial conditions
%         x(0)=[0], x(t)=[0], when t<0, 
%	  where [0] -- column-vector of zeros,
%         due to an initial condition on the states.
%	  It's equivalent to the system
%         .
%         x(t) = A0*x(t)+A1*y(-delay)+int(-delay,0,F(s)*y(s))ds
%		v(t) = C*x(t) 
%
%	  with the initial state x(0)=x0 and the initial function
%	  x(t), given by parameter initfun.
%  
%	  The time vector is automatically determined.  
%
%         When invoked with left hand arguments,
%            [T,V]=initiald(tf,x0,initfun,a0,a1,b,c,d,delay);
%            [T,V]=initiald(tf,x0,initfun,a0,a1,b,c,d,delay,F);
%            [T,V]=initiald(tf,x0,initfun,a0,a1,b,c,d,delay,F,tol);
%	  returns the time history in the vector T and the output in
%         the matrix V. No plot is drawn on the screen. V has as many
%         columns as there are outputs and length(T) rows.
%
%	  Invoked without left hand arguments INITIALD produces the graph.
%
%	  See also: STEPD, IMPULSED, INPUTD.


% Check the input parameters
if tf < 0 
  error('The first argument must be positive.'); 
end;
error(a0a1bcd(a0,a1,b,c,d));


% Compute the time vector and the corresponding state values
if nargin==9
  [tout,xout]=dde45l1(0,tf,x0,initfun,delay,a0,a1,...
                        zeros(length(x0),1));
end;
if nargin==10
  [tout,xout]=dde45l1(0,tf,x0,initfun,delay,a0,a1,...
                       zeros(length(x0),1),delay,F);
end;
if nargin==11
  [tout,xout]=dde45l1(0,tf,x0,initfun,delay,a0,a1,...
                       zeros(length(x0),1),delay,F,tol);
end;

% Compute the output 
vout=xout*c';


if nargout==0          % If no output arguments, plot graph
  plot(tout,vout)
  xlabel('Time (secs), t'), ylabel('Amplitude, v(t)')
  return    % Suppress output
end

T=tout;   
V=vout;