Table of Contents
Journal of Computational Methods in Physics
Volume 2013, Article ID 172906, 17 pages
Research Article

Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

1Department of Mathematics, Kovai Kalaimagal College of Arts and Science, Coimbatore, Tamil Nadu 641 109, India
2Department of Mathematics, Avinashilingam Deemed University for Women, Coimbatore, Tamil Nadu 641 043, India

Received 30 March 2013; Accepted 17 June 2013

Academic Editor: Ali Cemal Benim

Copyright © 2013 N. Mala and A. R. Sudamani Ramaswamy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.