Stability of sampled-data composite systems with many nonlinearities

Author

Araki, Mituhiko ; Ando, Kazuaki ; Kondo, Bunji

Author_Institution

Kyoto University, Yoshida, Kyoto, Japan

Volume

Issue

fYear

1971

fDate

2/1/1971 12:00:00 AM

Firstpage

Lastpage

Abstract

A sampled-data composite system given by a set of vector difference equations $x_{i}(\\tau + 1) - x_{i}(\\tau ) = \\sum \\min{j = 1} \\max {n} A_{ij} f_{j}[x_{j}(\\tau )], i = 1 ..., n$ is dealt with. The system given by $x_{i}(\\tau + 1) - x_{i}(\\tau ) = A_{ij} f_{i}[x_{i}(\\tau )]$ is referred to as the $i$ th isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the fisatisfy certain conditions and the leading principal minors of the determinant $|b_{ij}|, i,j = 1, ..., n,$ are all positive. Here, the diagonal element biiis a positive number such that $|x_{i}(\\tau + 1)| - |x_{i}(\\tau ) | \\leq - b_{ij}| f_{i}[x_{i}(\\tau )]|$ holds with regard to the motion of the $i$ th isolated subsystem, and the nondiagonal element $b_{ij} , i \\neq j$ , is the minus of $|A_{ij}|$ , which is defined as the maximum of $|A_{ij}x_{j}|$ , for $|x_{j}| = 1$ . 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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=805048