obs_gram

Scilab Function
Last update : 12/01/2004

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`,