Title :
Common Lyapunov functions and gradient algorithms
Author :
Liberzon, Daniel ; Tempo, Roberto
Author_Institution :
Coordinated Sci. Lab., Univ. of Illinois, Urbana, IL, USA
fDate :
6/1/2004 12:00:00 AM
Abstract :
This note is concerned with the problem of finding a quadratic common Lyapunov function for a large family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.
Keywords :
Lyapunov methods; convergence; gradient methods; linear matrix inequalities; linear systems; stability; time-varying systems; deterministic convergence; finite system families; gradient iteration algorithm; infinite families; linear matrix inequalities; probabilistic convergence; quadratic common Lyapunov functions; stable linear system; switched systems; Books; Convergence; Feedback; Iterative algorithms; Iterative methods; Linear matrix inequalities; Linear systems; Lyapunov method; Stability analysis; Time varying systems; Common Lyapunov functions; gradient algorithms; randomized algorithms; switched linear systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2004.829632
