A delayed neural network for solving linear projection equations and its analysis

Author

Liu, Qingshan ; Cao, Jinde ; Xia, Youshen

Author_Institution

Dept. of Math., Southeast Univ., Nanjing, China

Volume

16

Issue

4

fYear

2005

fDate

7/1/2005 12:00:00 AM

Firstpage

834

Lastpage

843

Abstract

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.

Keywords

Lyapunov methods; asymptotic stability; delays; differential equations; functional equations; linear matrix inequalities; neural nets; quadratic programming; Lyapunov Krasovskii theory; delayed neural network; functional differential equations; global asymptotic stability; global exponential stability; linear matrix inequality; linear projection equations; quadratic programming; Asymptotic stability; Computer networks; Convergence; Differential equations; Linear matrix inequalities; Mathematics; Neural networks; Quadratic programming; Stability analysis; Vectors; Asymptotical stability; Lyapunov–Krasovskii functional; delayed neural networks; exponential stability; linear matrix inequality (LMI); quadratic programming; Algorithms; Computer Simulation; Computing Methodologies; Linear Models; Models, Biological; Neural Networks (Computer); Numerical Analysis, Computer-Assisted; Programming, Linear; Time Factors;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/TNN.2005.849834

Filename

1461426