nnz.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 = nnz(varargin)
%NNZ (overloaded)
%   
%    n = nnz(X)
%
% The NNZ operator is implemented using the concept of nonlinear operators
% in YALMIP. NNZ(X) creates a new so called derived variable that can be
% treated as any other variable in YALMIP. When SOLVESDP is issued,
% logic constraints are added to the problem to model the NNZ operator. 

% Author Johan L鰂berg 
% $Id: nnz.m,v 1.6 2005/05/09 14:21:34 joloef Exp $   

switch class(varargin{1})
case 'char'
    z = varargin{2};
    x = varargin{3};
    
    [n,m] = size(x);
    F = set([]);
    totalcount = 0;
    if issymmetric(x)
        delta = binvar(n,n);  % delta==1 means x(i,j)==0         
        for i = 1:n
            for j = i:n
                xij=ihatethis(x,i,j);
                dij=ihatethis(delta,i,j);
                if isa(xij,'sdpvar')
                    F = F + set(implies(dij,xij==0));
                    if i==j
                        totalcount = totalcount + (1-dij);
                    else
                        totalcount = totalcount + 2*(1-dij);
                    end
                else
                    if xij~=0                        
                        if i==j
                            totalcount = totalcount + 1;
                        else
                            totalcount = totalcount + 2;
                        end                        
                    end
                end
            end
        end
    else
        delta = binvar(n,m);            
        for i = 1:n
            for j = 1:m
                xij=ihatethis(delta,i,j);
                dij=ihatethis(delta,i,j);
                if isa(xij,'sdpvar')                    
                    F = F + set(iff(dij,xij==0));
                    totalcount = totalcount + (1-dij);
                else
                    if xij~=0                        
                        totalcount = totalcount + 1;
                    end 
                end
            end
        end
    end
    depends(delta)
    F = F + set(z == totalcount);% + set(integer(z));    
    varargout{1} = F;
    varargout{2} = 0;
    varargout{3} = [];
    
case 'sdpvar'
    varargout{1} = yalmip('addextendedvariable','nnz',varargin{:});
    
otherwise
end