obs_gram - observability gramian

Calling Sequence

Go=obs_gram(A,C [,dom])

Go=obs_gram(sl)

Parameters

• A,C : real matrices (of appropriate dimensions)
• dom : string ("d' or "c" (default value))
• sl : syslin list

Description

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

Examples

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)
 

See Also

ctr_gram  obsvss  obsv_mat  lyap