mvpinv.m

MFD－多变量系统频域设计工具

function [ai,bi,ci,di] = mvpinv(a,b,c,d)
%MVPINV Pseudo-inverse of state-space system.
%
%       [ai,bi,ci,di] = mvpinv(a,b,c,d)
%
% Finds a state space model of a pseudo-inverse system.
% If the system has m inputs and n outputs, the matrix 'd'
% should have rank = min(m,n). If G is the transfer function
% of (a,b,c,d) and GI is the transfer function of [ai,bi,ci,di]
% then G*GI = I if m>=n, and GI*G = I if m<=n.
% (mvinv is better for square systems).

% J.M.Maciejowski, 22 March 1988.
% Copyright (c) 1988, Cambridge Control Ltd.

error(nargchk(4,4,nargin));
error(abcdchk(a,b,c,d));

di = pinv(d);
ai = a - b * di * c;
bi = b * di;  
ci = -di * c;