DocumentCode :
1192745
Title :
On the cross-Gramian for symmetric MIMO systems
Author :
Fernando, K.V. ; Nicholson, H.
Volume :
32
Issue :
5
fYear :
1985
fDate :
5/1/1985 12:00:00 AM
Firstpage :
487
Lastpage :
489
Abstract :
Recently, Laub et al. [1] and Fernando and Nicholson [2] extended the definition of the cross-Gramian matrix 
to include symmetric MIMO systems where the matrix is defined as an integral. In this correspondence, we define this matrix as a solution of a Lyapunov equation and prove the fundamental identity 
where 
and 
are the controllability and observability Gramians defined via Lyapunov equations. This definition of complements the integral definition and has some advantages from theoretical and numerical points of view.
to include symmetric MIMO systems where the matrix is defined as an integral. In this correspondence, we define this matrix as a solution of a Lyapunov equation and prove the fundamental identity where and are the controllability and observability Gramians defined via Lyapunov equations. This definition of complements the integral definition and has some advantages from theoretical and numerical points of view.Keywords :
Control systems; Matrices; Algebra; Circuit stability; Controllability; Integral equations; MIMO; Observability; Optical wavelength conversion; Signal processing; Speech processing; Symmetric matrices;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1985.1085737
Filename :
1085737
Link To Document :
