title: Passivity analysis of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters.
abstract: This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.
authors.affiliation: a Department of Mathematics , Thiruvalluvar University , Vellore , Tamil Nadu , India.
authors.forename: M Syed
authors.initials: MS
authors.lastname: Ali
authors.affiliation: a Department of Mathematics , Thiruvalluvar University , Vellore , Tamil Nadu , India.
authors.forename: M Esther
authors.initials: ME
authors.lastname: Rani
mesh_terms: D008390:Markov Chains; D016571:Neural Networks, Computer; D013269:Stochastic Processes; D013997:Time Factors
keywords: Delayed neural networks; Lyapunov functional; Markovian jumping parameters; linear matrix inequality; parameter uncertainty; passivity; stochastic disturbance; time-varying delays