Man Scilab

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 ,  

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