مرکز منطقه ای اطلاع رساني علوم و فناوري - Simplification of the Lyapunov matrix equation <img src="/images/tex/39.gif" alt="A_{T}PA

DocumentCode :

815214

Title :

Simplification of the Lyapunov matrix equation $A_{T}PA - P = -Q$

Author :

Barnett, Stephen

Author_Institution :

University of Bradford, Bradford, Yorkshire, England

Volume :

Issue :

fYear :

1974

fDate :

8/1/1974 12:00:00 AM

Firstpage :

446

Lastpage :

447

Abstract :

It is shown that in solving for the symmetric matrix $P$ the number of linear equations and unknowns can be reduced from $frac{1}{2}n(n + 1)$ to $frac{1}{2}n(n - 1)$ by introducing a skew-symmetric matrix. This corresponds to an earlier result for the equation $A_{1}^{T}P_{1} + P_{1}A = -Q$ .