本篇論文處理具有連續隨機擾動及不連續卜瓦松跳躍雜訊的非線性隨機偏微分系統處在時空域上的任意外界擾動和測量雜訊的環境下，提出一個強健H無窮大濾波器設計問題。對於非線性隨機偏微分系統而言，透過測量輸出設計一個H無窮大濾波設計問題是必須去求得一個複雜的二階漢米爾頓-傑克比積分不等式。為了要化簡設計程序，一個模糊內插方法的模糊隨機偏微分系統被提出來近似非線性隨機偏微分系統。然後，一個強健H無窮大濾波設計問題可以被轉換成擴散矩陣不等式問題。為了透過傳統代數矩陣技巧來解困難的擴散矩陣不等式，我們使用發散定理及龐加萊不等式將擴散矩陣不等式轉換成雙線性矩陣不等式，雙線性矩陣不等式可以藉由所提出的去耦合技術轉換成線性矩陣不等式來化簡非線性隨機偏微分系統強健H無窮大模糊濾波器的設計程序。對於強健H無窮大模糊濾波器所提出的設計方法是可以被有效的壓制在非線性隨機偏微分系統中時空域上的外來雜訊干擾。最後，一個在時空域上受到連續布朗運動以及不連續卜瓦松跳躍擾動的生態系統被用來驗證設計程序以及確認所提出的強健H無窮大模糊濾波設計方法的狀態估測效能。

This paper addresses a robust H-infinity fuzzy filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with continuous random fluctuations, discontinuous Poisson jumping noise, random external disturbance and measurement noise in the spatio-temporal domain. For NSPDSs, the robust H-infinity filter design problem through a measurement output needs to solve a complex second-order Hamilton Jacobi integral inequality (HJII). In order to simplify the design procedure, a fuzzy stochastic partial differential system (FSPDS) based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, the robust H-infinity fuzzy filter design problem can be reformulated as a diffusion matrix inequality (DMI) problem. To solve a set of difficult DMIs for the H-infinity fuzzy filter via the traditional algebraic matrix techniques, we utilize the divergence theorem and Poincare inequality to transform the DMIs into bilinear matrix inequalities (BMIs), which could be easily transformed to a set of equivalent linear matrix inequalities (LMIs) by the proposed decoupling technique to simplify the design procedure of robust H-infinity fuzzy filter for NSPDSs. The proposed robust H-infinity fuzzy filter could efficiently attenuate the effect of spatio-temporal external disturbances on the filtering performance of NSPDSs. Finally, a robust state estimation problem of an ecology system with intrinsic spatio-temporal continuous Wiener noise and discontinuous Poisson jump fluctuations is provided to illustrate the design procedure and to confirm the H-infinity filtering performance of the proposed H-infinity fuzzy filter design method.

摘要--------------------------------------------------(i)
Abstract---------------------------------------------(ii)
誌謝------------------------------------------------(iii)
Contents---------------------------------------------(iv)
I.Introduction------------------------------------------1
II.Preliminaries and Problem Formulation----------------5
III.Robust Filter Design for NSPDS by Fuzzy Approach---10
IV.A New Design Method for Robust Fuzzy Filter of NSPDSs-------------------------------------------------14
V.Simulation Results-----------------------------------17
VI.Conclusions---------------------------------------- 23
Reference----------------------------------------------24
Appendix---------------------------------------------- 27

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