%LMIINFO Get information about an existing system of LMIs % % LMIINFO(LMISYS) Gives information about the system of LMI defined in % LMISYS. This includes information about: % * the variable matrices (dimensions and structure) % * the block structure and dimensions of the LMIs % * the term content of each LMI % % See also LMIEDIT, LMINBR, MATNBR, DECNBR. % Author: A. Ignat 1/94 % Copyright 1995-2004 The MathWorks, Inc. % $Revision: 1.1.6.1 $ function lmiinfo(LMIsys) if nargin~=1, error('usage: lmiinfo(lmisys)'); end [LMI_set,LMI_var,LMI_term,data]=lmiunpck(LMIsys); if isempty(LMI_set), error('LMISYS contains no information on the LMI dimensions'); elseif isempty(LMI_var), error('LMISYS contains no information on matrix variables'); elseif isempty(LMI_term), error('LMISYS contains no information on LMI terms'); end disp(sprintf('\n\n LMI ORACLE \n')); top = 0 ; writevar = [' This is a system of ', num2str(size(LMI_set,2)),... ' LMI(s) with ',num2str(size(LMI_var,2)),' matrix variables']; disp(' -------------- '); disp(sprintf('\n%s\n',writevar)) ; disp(sprintf(' Do you want information on ')); disp(' (v) matrix variables (l) LMIs (q) quit '); rep = input('?> ','s'); while length(rep)~=1 | ~any(rep==['v' 'V' 'l' 'L' '1' 'q' 'Q']), disp(' (v) matrix variables (l) LMIs (q) quit '); rep = input('?> ','s'); end while rep ~= 'q' & rep ~= 'Q' if any(rep == ['v' 'V']), % info about variable matrices: structure, dimensions nrvarm = goodans(1,size(LMI_var,2),... ' Which variable matrix (enter its index k between ',1) ; writevar = [' X',num2str(nrvarm),' is a ']; if LMI_var(2,nrvarm) == 1 if LMI_var(5,nrvarm) == 1 & LMI_var(6,nrvarm) == 1 writevar = [' x',num2str(nrvarm),' is a scalar variable\n']; disp(sprintf(writevar)); else writevar = [writevar,num2str(LMI_var(5,nrvarm)),'x',... num2str(LMI_var(6,nrvarm)),' symmetric block diagonal matrix']; disp(sprintf(writevar)); %the block structure of on symmetric block diagonal variable for i = 1:LMI_var(7,nrvarm) writevar = ... [' its (',num2str(i),',',num2str(i),')-block is a ']; if LMI_var(9+(i-1)*2,nrvarm) == 0 writevar = [ writevar,'scalar block t*I of size ']; elseif LMI_var(9+(i-1)*2,nrvarm) == 1 writevar = [ writevar,'full block of size ']; elseif LMI_var(9+(i-1)*2,nrvarm) == -1, writevar = [ writevar,'zero block of size ']; else disp(sprintf(' Error in variable definition: unknown block type')); end writevar = [writevar,num2str(LMI_var(8+(i-1)*2,nrvarm))]; disp(writevar); end disp(' '); end elseif LMI_var(2,nrvarm) == 2 writevar = [writevar,num2str(LMI_var(5,nrvarm)),'x', ... num2str(LMI_var(6,nrvarm)),' rectangular matrix\n']; disp(sprintf(writevar)); elseif any(LMI_var(2,nrvarm) == [31 32]), writevar = [writevar,'matrix of type 3\n']; disp(sprintf(writevar)); else disp(' Error in variable definition: type of structure unknown'); return; end elseif any(rep == ['l' '1' 'L']), % info ablout an LMI nrlmi = goodans(1,size(LMI_set,2),... ' Which LMI (enter its number k between ',1); % checks for left, right side existence and left, right % inner factor presence lmilb=LMI_set(1,nrlmi); islside=any(LMI_term(1,:)==lmilb); % LHS ~=0 isrside=any(LMI_term(1,:)==-lmilb); % RHS ~=0 % Look for outer factor indof = find(abs(LMI_term(1,:))==lmilb & LMI_term(2,:)==0); isoutf = ~isempty(indof); if isoutf ptr = LMI_term(5,indof(1)); % start of outer factor record in DATA rN=data(ptr+1); cN=data(ptr+2); % outer factor dims end if islside == 0 % left side = 0 writevar = [' 0 < ']; elseif isoutf == 0 % no left outer factor writevar = [' L(x) < '] ; else % left side with outer factor writevar = [' N'' * L(x) * N < '] ; end if isrside == 0 % right side = 0 writevar = [writevar,' 0 ']; elseif isoutf == 0 % no right outer factor writevar = [writevar,' R(x) '] ; else % right side with outer factor writevar = [writevar,' M'' * R(x) * M '] ; end disp(sprintf(' This LMI is of the form \n')) ; disp(sprintf('%s\n',writevar)) ; writevar =[' where the inner factor(s) has ', ... num2str(LMI_set(6,nrlmi)),' diagonal block(s)'] ; disp(writevar); if isoutf writevar = [' the outer factor(s) is of size ',... num2str(rN),'x',num2str(cN)]; disp(writevar); end disp(sprintf('\n\n')); %info about the inner factor(s) % choose the inner factor switch islside + isrside case 2 disp(sprintf(' Do you want info on the inner factors ?\n')); rlif = 'Z' ; while ~any(strcmpi(rlif,{'r','l','t','o'})) disp(sprintf(' (l) left (r) right (o) other LMI (t) back to top level ')); rlif = input('?> ','s'); end while any(strcmpi(rlif,{'r','l'})) disp(' '); lminf = 'Z'; while ~any(strcmpi(lminf,{'b','w'})) disp(' You want to see: (w) the whole factor (b) only one block ?'); lminf = input('?> ','s'); end infobw(LMI_set,LMI_var,LMI_term,data,nrlmi,rlif,lminf) ; rlif = 'Z' ; while ~any(strcmpi(rlif,{'r','l','t','o'})) disp(sprintf('\n Do you want info on the inner factors ?\n')); disp(sprintf(' (l) left (r) right (o) other LMI (t) back to top level ')); rlif = input('?> ','s'); end end %while rlif == 'l'| 'r' if strcmpi(rlif,'o') top = 1; end case 1 if islside == 0 rlif = 'r' ; writevar=[' right']; else rlif = 'l' ;writevar=[' left']; end disp(sprintf(' Do you want info on the%s inner factor ?\n',writevar)); lminf = 'Z'; while ~any(strcmpi(lminf,{'b','w','t','o'})) disp(' (w) whole factor (b) only one block '); disp(' (o) other LMI (t) back to top level '); lminf = input('?> ','s'); end while any(strcmpi(lminf,{'w','b'})) infobw(LMI_set,LMI_var,LMI_term,data,nrlmi,rlif,lminf) ; lminf = 'Z'; while ~any(strcmpi(lminf,{'b','w','t','o'})) disp(' (w) whole factor (b) only one block '); disp(' (o) other LMI (t) back to top level '); lminf = input('?> ','s'); end end % while lminf = 'w' | 'b' if strcmpi(lminf,'o') top = 1; end otherwise disp(sprintf(' LMI %i : 0 < 0 !\n',nrlmi)) ; end end %if rep if top == 0 writevar = [' This is a system of ', num2str(size(LMI_set,2)),... ' LMI with ',num2str(size(LMI_var,2)),' variable matrices']; disp(' -------------- '); disp(sprintf('\n%s\n',writevar)) ; disp(sprintf(' Do you want information on ')); rep = 't' ; while ~any(strcmpi(rep,{'v','1','l','q'})) disp(' (v) matrix variables (l) LMIs (q) quit '); rep = input('?> ','s'); end else top = 0; end end % while rep disp(' '); disp(sprintf(' It has been a pleasure serving you!\n'));