observability gramian
Go=obs_gram(A,C [,dom])
Go=obs_gram(sl)
:A,C real matrices (of appropriate dimensions) : :dom string ( “d’ or “c” (default value)) : :sl syslin list :
Observability gramian of the pair (A,C) or linear system sl ( syslin list). dom is the domain which can be
:”c” continuous system (default) : :”d” discrete system :
A=-`diag`_(1:3);C=`rand`_(2,3);
Go=obs_gram(A,C,'c'); // <=> w=syslin('c',A,[],C); Go=obs_gram(w);
`norm`_(Go*A+A'*Go+C'*C,1)
`norm`_(`lyap`_(A,-C'*C,'c')-Go,1)
A=A/4; Go=obs_gram(A,C,'d'); //discrete time case
`norm`_(`lyap`_(A,-C'*C,'d')-Go,1)