 
Summary: A note on the Lyapunov Equation
Alessandro Abate
a.abate@tudelft.nl
Delft Center for Systems and Control, TU Delft
October 27, 2011
Ac.Yr. 2011/12, 1e Sem. Q1 Note sc4026
A. Abate
Consider a given state space matrix A, in general not
symmetric.
The Lyapunov equation is given by
AT
P + P A = Q1, (1)
where Q1 is a given positive definite matrix, and P the solution
of the above equation.
It has been brought to my attention that MATLAB instead
solves
AX + XA
T
= Q2 (2)
(see documentation for a confirmation). Here Q2 is a given
