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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/35712

Title: 具馬可夫參數脈衝及時變延遲之隨機基因調控網路漸進穩定度探討
Asymptotic Stability Analysis of Markovian Jumping Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delays
Authors: 林湧傑
Contributors: NTOU:Department of Communications Navigation and Control Engineering
國立臺灣海洋大學:通訊與導航工程學系
Keywords: 基因調控網路;線性矩陣不等式;脈衝;馬可夫參數;模型不確定性;蕭氏轉換
genetic regulatory network;linear matrix inequality;impulse;Markovian jumping;model uncertainty;Schur complements
Date: 2012
Issue Date: 2013-10-07T02:58:09Z
Abstract: 本論文旨在利用李亞普諾函數針對具馬可夫參數脈衝及時變延遲之隨機基因調控網路推導出新的漸進穩定度準則。SUM調控網路將被用於表示基因調控機制且馬可夫鏈將用於表示混和狀態基因調控網路。針對不確定性且帶有時間延遲的基因調控網路,結構的不確定非線性函數將用來表示建模之誤差。此外,具脈衝的基因調控網路將以連續及不連續部分的時間區間分開討論。藉由引入邊界不等式技巧及自由矩陣,新的穩定度定理可適用於快速及緩慢的時間延遲。另一方面,利用馬可夫跳躍參數及隨機微分方程式理論,帶有馬可夫參數之隨機基因調控網路可被解析。接著根據傑生積分公式和自由分佈函數將推導出較不保守的穩定度定理且所有的穩定性條件皆可藉由蕭氏轉換公式輕易轉換成線性矩陣不等式。最後,數值模擬的例題將用於驗證所提定理的效能。
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.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0019967042
http://ntour.ntou.edu.tw/handle/987654321/35712
Appears in Collections:[通訊與導航工程學系] 博碩士論文

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