Asymptotic Stability Analysis of Markovian Jumping Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delays

• Main Author: 林湧傑
• Other Authors: Cheng-Fa Cheng
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/63174021217595304456

碩士 === 國立臺灣海洋大學 === 通訊與導航工程學系 === 100 === The purpose of this thesis is to investigate new robust stability criteria of Markovian jumping impulsive stochastic genetic regulatory networks with time-varying delays based on Lyapunov functional. The SUM regulatory functions are utilized to model the regulatory mechanism and the Markov chain process is regarded as hybrid genetic regulatory networks. For the uncertain genetic regulatory network, structured nonlinear uncertainty functions are employed to present model uncertainties. Besides, the impulsive genetic regulatory networks will be discussed by separating time interval into continuous and discontinuous parts. The stability of genetic regulatory networks with fast and slow time-varying delays will be explored by introducing inequality bounding techniques and free weighting matrices. On the other hand, the Markovian jumping stochastic regulatory networks will be analyzed by using stochastic differential equation theory and Morakvian jumping parameters. Furthermore, the conservatism of the criteria can be reduced by utilizing Jensen’s integral formula and free distribution parameters. All the proposed stability conditions can be easily expressed in terms of linear matrix inequality (LMIs) by Schur complements. Finally, numerical examples are given to show the effectiveness of the proposed criteria.