r2pq.m

A Matlab toolbox for exact linear time-invariant system identification is presented. The emphasis is

% R2PQ - From kernel to LMF representation.
%
%  [P,Q] = pq2ss(R)
%
% R - 3d array of parameter of a kernel representation
%     ( R0 = R(:,:,1), ... ,Rl = R(:,:,l+1) )
% P,Q - 3d array of parameters of an LMF representation
%     ( the same format as R )
%
% Note 1: the input/output partition is fixed-first 
% M variables inputs, the rest outputs.
%
% Note 2: requires the Polynomial Toolbox Version 1.5

function [P,Q] = pq2ss(R)

% Constants
[g,dw,l1]  = size(R);
l  = l1 - 1;

% Find a minimal kernel representation (R row reduced)
addpath ../polyx

% Unfold R in a 2d matrix [R0 R1 ... Rl]
R = reshape(R,g,(l1)*dw);

% Call polyx for the row reduction
R = ppck(R,l);
R = prowred(R,'z');

% Cancel zero rows
p = prank(R);
R = psel(R,1:p,':');
R = punpck(R);

% Transform R back to a 3d array
R = reshape(R,p,dw,l1);

% Partition R
m = dw - p;
Q = R(:,1:m,:);
P = -R(:,m+1:end,:);