Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
2025.0.0 - English


lyap

Lyapunov equation

Syntax

[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 — Solve the Sylvester equations A*X + X*B = C or A*X*B + X = C
  • ctr_gram — controllability gramian
  • obs_gram — observability gramian
Report an issue
<< kroneck Matrix Pencil pen2ea >>

Copyright (c) 2022-2024 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 24 11:13:08 CEST 2024