Stability Analysis for Switched Boolean Networks Under Arbitrary Switching Signals

Author

Haitao Li ; Yuzhen Wang ; Zhenbin Liu

Author_Institution

Sch. of Control Sci. & Eng., Shandong Univ., Jinan, China

Volume

59

Issue

7

fYear

2014

fDate

Jul-14

Firstpage

1978

Lastpage

1982

Abstract

This note investigates the stability of switched Boolean networks (SBNs) under arbitrary switching signal by using the tool of semi-tensor product of matrices. First, an algebraic expression is given for the SBN via the semi-tensor product. Based on it, a necessary and sufficient condition is presented for the switching point reachability of the system. Second, using the switching point reachability, the pointwise stabilizability is studied, and a necessary and sufficient condition is obtained. Finally, the global stability of SBNs under arbitrary switching signal is investigated, and an easily verifiable necessary and sufficient condition is presented. Two illustrative examples are presented to show that the main results are effective in analyzing the stability of SBNs.

Keywords

Boolean functions; matrix algebra; reachability analysis; stability; tensors; time-varying systems; SBN; algebraic expression; arbitrary switching signal; global stability; matrices; necessary condition; pointwise stabilizability; semitensor product; stability analysis; sufficient condition; switched Boolean networks; switching point reachability; Stability criteria; Switches; Trajectory; Vectors; Xenon; Pointwise stabilizability; semi-tensor product; stability; switched Boolean network (SBN); switching point reachability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2298731

Filename

6704704