geomean2.m

国外专家做的求解LMI鲁棒控制的工具箱,可以相对高效的解决LMI问题

function varargout = geomean2(varargin)
%GEOMEAN2 Nonlinear operator in YALMIP
%
% t = geomean2(X)
%
% For Hermitian matrix X, returns det(X)^(1/(2^ceil(log2(length(X)))))
%
% For real vector X, returns prod(X)^(1/(2^ceil(log2(length(X)))))
%
% This concave function is monotonically growing in det(P)
% for P>0, so  it can be used for maximizing det(P), 
% or to add lower bound constraints on the determinant.
%
% Note also that the function is the geometric mean of
% the elements (or eigenvalues) if the dimension of 
% X is a power of 2, hence the name GEOMEAN2
%
% See also SDPVAR, SUMK, SUMABSK

% Author Johan L鰂berg
% $Id: geomean2.m,v 1.6 2005/02/08 16:11:17 johanl Exp $

% ***************************************************
% This file defines a nonlinear operator for YALMIP
%
% It can take three different inputs
% For double inputs, it returns standard double values
% For sdpvar inputs, it genreates a an internal variable
% When first input is 'model' it generates the (hypo or epi)graph
%
% ***************************************************
switch class(varargin{1})
    
case 'double' % What is the numerical value of this argument (needed for displays etc)        
    X = varargin{1};
    [n,m] = size(X);
    if min(n,m)==1
        varargout{1} = prod(X)^(1/(2^ceil(log2(length(X)))));
    else
        if norm(X-X')<n*eps
            varargout{1} = (real(det(X)))^(1/(2^ceil(log2(length(X)))));
        else
            error('GEOMEAN2 can only be applied to real vectors and Hermitian matrices');
        end
    end
    
case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them.
    X = varargin{1};
    [n,m] = size(X);
    if is(varargin{1},'hermitian') | min(n,m)==1
        varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:});    
    else
        error('GEOMEAN2 can only be applied to real vectors and Hermitian matrices');
    end
    
case 'char' % YALMIP send 'model' when it wants the epigraph or hypograph
    if isequal(varargin{1},'graph')
        t = varargin{2}; % Second arg is the extended operator variable
        X = varargin{3}; % Third arg and above are the args user used when defining t.           
        varargout{1} = detset(t,X);
        varargout{2} = -1; % Concave operator            
    else           
    end    
otherwise
end