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Scilab help >> Linear Algebra > lyap

# lyap

Lyapunov equation

### Calling Sequence

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

### Arguments

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 — Sylvester equation.
• ctr_gram — controllability gramian
• obs_gram — observability gramian

### Comments

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