lyap

Scilab Function
Last update : April 1993

lyap - Lyapunov equation

### Calling Sequence

  `[X]=lyap(A,C,'c')`
  `[X]=lyap(A,C,'d')`

### Parameters

- `A, C` : real square matrices, `C` must be symmetric

### Description

`X = lyap(A,C,flag)` solves the continuous time or discrete time matrix Lyapunov matrix equation:

           A'*X + X*A = C       ( flag='c' )
          A'*X*A - X = C       ( flag='d' )

Note that a unique solution exist if and only if an eigenvalue of `A` is not an eigenvalue of `-A` (`flag='c'` ) or 1 over an eigenvalue of `A` (`flag='d'` ).

### Examples

    A=rand(4,4);C=rand(A);C=C+C';
    X=lyap(A,C,'c');
    A'*X + X*A -C
    X=lyap(A,C,'d');
    A'*X*A - X -C

### See Also

`sylv` , `ctr_gram` , `obs_gram` ,