Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng

MINISTRY OF EDUCATION AND TRAINING

QUY NHON UNIVERSITY

DAO THI HAI YEN

ON THE STATE ESTIMATION PROBLEM FOR SOME CLASSES OF DYNAMICAL Systems and ITS APPLICATION

DOCTORAL THESIS IN MATHEMATICS

Binh Dinh – 2023

Declaration

This thesis was completed at the Department of Mathematics and Statistics, Quy Nhon University under the guidance of Assoc. Prof. Dinh Cong Huong. 1 hereby declare that the results presented in here are new and original Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng . All of them were published in peer-reviewed journals and conferences. For using results from joint papers I have gotten permissions from my co-authors.

Dinh Dinh. 2023

PhD student

Dao Thỉ Hai Yen

Acknowledgments

First, I would like to express my gratitude to the two offices Phu Yen University, my workplace, and Quy Nhon University, where I have leamt and studied tor a long time. I would also like to express my gratitude* to all people working Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng al the Department OÍ Postgraduate 1 ruining and die Department of Mathematics and Statistics OÍ Quy Mhon University.

Next, the thesis was carried out during rhe years I have been a PhD student at rhe Department of Mathematics and Statistics, Quy Nhon University. On rhe occasion of completing rhe thesis, T would like to express rhe deep grarinide to Assoc. Prof. Dr. Dinh Cong Huong nor only for his reaching and scientific leadership, hut also for rhe helping me access to rhe academic environment through Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng rhe workshops, mini courses that assist me in broadening my thinking to ger rhe entire view on rhe related issues in my research.

Finally, 1 wish to acknowledge my father, my paients in law for supporting me in every decision. And, my enormous gratitude goes to my husband and sons for their love and patience during the rime I was working intensively to complete my PhD program. Finally, my sincere thank goes to my mother for guiding me to math and this thesis is dedicated to Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng her.

Contents

Table of Notations

List of drawings

Introduction

• 1    Preliminaries

• 1.1   Some basic concepts

• 1.1.1  Stability criteria of some classes of dynamic systems

• 1.1.2  Additional lemmas

• 1.2    State observer design problems

• 1.2.1   Full order state observer

• 1.2.2  Reduced order state observer

• 1.2.3   Linear functional state observer

• 1.2.4  Interval observer

• 2    A new method for designing observers of a nonlinear time-delay Glucose-

Insulin sys- tern

• 2.1    Bài toán ước lượng trạng thái cho một số lớp hệ động lực và áp dụng A novel state transformation

• 2.2   Application to theGI     model

• 2.2.1   State transformation for the Gl model

• 2.2.2  State observer design for the GI model

• 2.2.3  Simulation results

• 3    A new observer for interconnected time-delay systems and its applications to

fault detection problem

• 3.1    New state transformation

• 3.2    Fault detection observer

• 3.3   A numerical example

• 4 Distributed functional interval observer design for large-scale networks

impulsive sys- terns..

• 4.1    Designing Bài toán ước lượng trạng thái cho m ột số lớp hệ động lực và áp dụng distributed linear… functional

interval                     observers S3

• 4.2    Existence conditions of distributed linearfunctionalinterval observers

• 4.3   Solving unknown matrices

• 4.4   Numerical examples

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