DocumentCode :
832630
Title :
Lyapunov functions for a class of large-scale systems
Author :
Sinha, A.S.C.
Author_Institution :
Indiana University-Purdue University, Indianpolis, IN, USA
Volume :
25
Issue :
3
fYear :
1980
fDate :
6/1/1980 12:00:00 AM
Firstpage :
558
Lastpage :
560
Abstract :
The behavior of solutions of a class of large-scale systems with the bounded coefficients of the form [1] has been studied. The function 
, whose coefficient 
is bounded for all 
, gives the conditions on the Lyapunov function such that the system (1) is either asymptotically stable or unstable. Since the function of the form 
is not positive definite in the Lyapunov sense, a Lyapunov function of the form 
where 
is bounded is constructed which is positive definite in the Lyapunov sense. A systematic procedure for the construction of such a function is given. The approach is quite general. The method is inspired from the papers of Grujic and Siljak [1], Siljak [2], [3], Weissenberger [4], Bailey [5], and Michel et al. [7], [8].
, whose coefficient is bounded for all , gives the conditions on the Lyapunov function such that the system (1) is either asymptotically stable or unstable. Since the function of the form is not positive definite in the Lyapunov sense, a Lyapunov function of the form where is bounded is constructed which is positive definite in the Lyapunov sense. A systematic procedure for the construction of such a function is given. The approach is quite general. The method is inspired from the papers of Grujic and Siljak [1], Siljak [2], [3], Weissenberger [4], Bailey [5], and Michel et al. [7], [8].Keywords :
Asymptotic stability; Interconnected systems; Lyapunov functions; Nonlinear systems, continuous-time; Differential equations; Large-scale systems; Lyapunov method; Stability; Sufficient conditions; Tellurium;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1980.1102356
Filename :
1102356
Link To Document :
