Descriptor Lyapunov inequalities

  In the study of descriptor systems, it is sometimes necessary to find (or find out that it does not exist) an matrix X satisfying

where E and A are matrices such that E,A is a regular pencil. In this problem, which clearly is a problem, the LME functions play important role. The evaluation function can be written as follows

function [LME,LMI,OBJ]=dscr_lyap_eval(XLIST)
X=XLIST(:)
LME=E'*X-X'*E
LMI=list(-A'*X-X'*A-eye,E'*X)
OBJ=[]

and the problem can be solved by (assuming E and A are already defined)

--> XLIST0=list(zeros(A))
--> XLISTF=lmisolver(XLIST0,dscr_lyap_eval)
--> X=XLISTF(:)