Singularly Perturbed Jump Systems: Stability, Synchronization and Control

✍ Scribed by Hao Shen, Ju H. Park, Feng Li, Jing Wang

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 250
• Series: Studies in Systems, Decision and Control
• Category: Library

✦ Synopsis

In this book, various singularly perturbed jump system models in continuous-time or discrete-time domain, such as Markov jump singularly perturbed systems, semi-Markov jump singularly perturbed systems, hidden Markov jump singularly perturbed systems, and singularly perturbed jump complex network model, have been considered for some control synthesis problems. Also, some partial probability information cases are taken into account when addressing those control synthesis problems. To show the effectiveness and applicability of the obtained results, some numerical examples and practical industrial model examples are given.

✦ Table of Contents

Acknowledgements
Contents
Symbols
1 Introduction and Preview
1.1 Motivation and Background
1.2 Mathematical Descriptions and Basic Concepts
1.2.1 Continuous-Time Singularly Perturbed Jump Systems
1.2.2 Discrete-Time Singularly Perturbed Jump Systems
1.2.3 Lemmas
1.3 Literature Review
1.3.1 Stability and Stabilization
1.3.2 Robust Control
1.3.3 Filtering, State Estimation and Synchronization
1.4 Organization of the Book
Part I Markov Jump Singularly Perturbed Systems
2 Stochastic Stability Analysis and Stabilization
2.1 Problem Formulation
2.2 Stochastic Stability Analysis
2.2.1 Complete Probability Information Case
2.2.2 Partial Probability Information Case
2.2.3 General Probability Information Case
2.3 Stabilization
2.3.1 Complete Probability Information Case
2.3.2 Partial Probability Information Case
2.3.3 General Probability Information Case
2.4 Numerical Examples
2.5 Summary
3 Control of Linear Systems Case
3.1 Problem Formulation
3.2 upper H Subscript normal infinityHinfty Control
3.2.1 Complete Probability Information Case
3.2.2 Partial Probability Information Case
3.2.3 General Probability Information Case
3.3 Numerical Example
3.4 Summary
4 Control of Nonlinear Systems Case
4.1 Problem Formulation
4.2 Robust Control
4.2.1 Nonfragile upper H Subscript normal infinityHinfty Control
4.2.2 Nonfragile Passive Control
4.2.3 upper H Subscript normal infinityHinfty Fault-Tolerant Control
4.3 Numerical Examples
4.4 Summary
5 Synchronization of Complex Networks Case
5.1 Problem Formulation
5.2 upper H Subscript normal infinityHinfty Synchronization
5.3 A Numerical Example
5.4 Summary
Part II Semi-Markov Jump Singularly Perturbed Systems
6 Stabilization of Linear Systems Case
6.1 Problem Formulation
6.2 Stabilization
6.2.1 Complete Probability Information Case
6.2.2 Partial Probability Information Case
6.3 Numerical Examples
6.4 Summary
7 Stabilization of Nonlinear Systems Case
7.1 Problem Formulation
7.2 Stabilization
7.2.1 Complete Probability Information Case
7.2.2 Partial Probability Information
7.3 Numerical Examples
7.4 Summary
8 upper H Subscript normal infinityHinfty Synchronization of Complex Networks Case
8.1 Problem Formulation
8.2 upper H Subscript normal infinityHinfty Synchronization
8.3 Numerical Example
8.4 Summary
Part III Hidden Markov Jump Singularly Perturbed Systems
9 HSubscript normal infinityinfty Control of Linear Systems Case
9.1 Problem Formulation
9.2 upper H Subscript normal infinityHinfty Control
9.2.1 Complete Probability Information Case
9.2.2 Partial Probability Information Case
9.2.3 General Probability Information Case
9.3 A Numerical Example
9.4 Summary
10 HSubscript normal infinityinfty Control of Nonlinear Systems Case
10.1 Problem Formulation
10.2 upper H Subscript normal infinityHinfty Control
10.2.1 Complete Probability Information Case
10.2.2 Partial Probability Information Case
10.2.3 General Probability Information Case
10.3 Numerical Examples
10.4 Summary
11 Finite-Time Control Case
11.1 Problem Formulation
11.2 Finite-Time Control
11.2.1 Complete Probability Information Case
11.2.2 Partial Probability Information Case
11.2.3 General Probability Information Case
11.3 Numerical Example
11.4 Summary
Appendix References