DocumentCode :
805048
Title :
Stability of sampled-data composite systems with many nonlinearities
Author :
Araki, Mituhiko ; Ando, Kazuaki ; Kondo, Bunji
Author_Institution :
Kyoto University, Yoshida, Kyoto, Japan
Volume :
16
Issue :
1
fYear :
1971
fDate :
2/1/1971 12:00:00 AM
Firstpage :
22
Lastpage :
27
Abstract :
A sampled-data composite system given by a set of vector difference equations ![x_{i}(\\tau + 1) - x_{i}(\\tau ) = \\sum \\min{j = 1} \\max {n} A_{ij} f_{j}[x_{j}(\\tau )], i = 1 ..., n](/images/tex/5613.gif)
is dealt with. The system given by ![x_{i}(\\tau + 1) - x_{i}(\\tau ) = A_{ij} f_{i}[x_{i}(\\tau )]](/images/tex/5614.gif)
is referred to as the 
th isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the fi satisfy certain conditions and the leading principal minors of the determinant 
are all positive. Here, the diagonal element bii is a positive number such that ![|x_{i}(\\tau + 1)| - |x_{i}(\\tau ) | \\leq - b_{ij}| f_{i}[x_{i}(\\tau )]|](/images/tex/5616.gif)
holds with regard to the motion of the th isolated subsystem, and the nondiagonal element 
, is the minus of 
, which is defined as the maximum of 
, for 
. Some extensions of this result are also given. Composite relay controlled systems are studied as examples.
is dealt with. The system given by is referred to as the th isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the f are all positive. Here, the diagonal element b holds with regard to the motion of the th isolated subsystem, and the nondiagonal element , is the minus of , which is defined as the maximum of , for . Some extensions of this result are also given. Composite relay controlled systems are studied as examples.Keywords :
Asymptotic stability; Discrete-time systems, nonlinear; Interconnected systems; Nonlinear systems, discrete-time; Asymptotic stability; Control nonlinearities; Control systems; Difference equations; Electrical equipment industry; Industrial control; Interconnected systems; Large-scale systems; Nonlinear control systems; Relays;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1971.1099623
Filename :
1099623
Link To Document :
