非线性物理科学 混合系统理论 确定系统和随机系统 英文版
作者： （加）穆罕默德·阿尔万（Mohamad S.Alwan），（加）刘新芝著
出版时间：2019年版
内容简介
本书介绍了确定性和随机混合系统的理论。混合系统是一个横跨应用数学、控制科学和计算机科学等学科的交叉研究领域。在此类系统中，若干个连续过程与不同层次的自动化设备相互作用。这些自动化装置起着监督、管理和决策作用，从而构成多个离散事件过程，这些集若干连续过程与若干离散过程为一体的大型反应系统即构成一个混合系统。混合系统的理论为大型反应系统提供了一个很好的数学模型，它是一个非常有价值的建模工具，可用于描述广泛的现实世界的应用。本书介绍了多个 Lyapunov或Razumikhin–Lyapunov函数方法，讨论了确定性和随机混合系统领域的极新发展。本书还论述了系统的稳定性、稳定化、可靠控制、输入-状态稳定性(ISS) 稳定化、状态估计和大规模奇异摄动系统的稳定性等性质。
目录
1 Motivating Examples
1.1 Switched Systems
1.1.1 Supervisory Switching Control
1.1.2 Switched Server System
1.1.3 Singular System with Markov Switching
1.2 Impulsive Systems
1.2.1 SEIRS Epidemic Model with Impulse Vaccinations
1.2.2 Insulin Treatment
References
2 Mathematical Background
2.1 Basic Definitions
2.2 Comparison Method
2.3 Delay Systems
2.4 Impulsive Systems
2.5 Comparison Method for Impulsive Systems
2.6 Impulsive Systems with Time Delay
2.7 Stochastic Differential Equations
2.7.1 Notations and Basic Definitions
2.7.2 Stochastic Processes
2.7.3 Stochastic Differential Equations
2.7.4 Comparison Method for Stochastic Systems
2.8 Stochastic Impulsive System with Time Delay
2.9 Switched Systems
2.9.1 System Formulation
2.9.2 Systems with Stable Subsystems
2.10 Stochastic Switched Systems with Time Delay
2.11 Singularly Perturbed Systems
2.12 Miscellaneous Results
2.13 Notes and Comments
References
3 Fundamental Properties of Stochastic Impulsive Systems with Time Delay
3.1 Existence of Solution
3.2 Forward Continuation
3.3 Global Existence
3.4 Uniqueness of Solution
3.5 Notes and Comments
References
4 Stability of Stochastic Impulsive Systems with Time Delay
4.1 Stability Analysis by Classical Lyapunov Technique
4.2 Stability Analysis by Comparison Method
4.3 Notes and Comments
References
5 Large-Scale Stochastic Impulsive Systems with Time Delay
5.1 Problem Formulation
5.2 Analysis by Lyapunov Method
5.3 Comparison Method
5.3.1 Method of Lyapunov Function
5.3.2 Method of Vector Lyapunov Functions
5.4 Examples
5.5 Notes and Comments References
6 Input-to-State Stability for Stochastic Switched Systems
6.1 Problem Formulation
6.2 Initial-State-Dependent Dwell-Time
6.3 Markovian Switching
6.4 Notes and Comments
References
7 Reliable Control for Stochastic Switched Systems with State Delay
7.1 Problem Formulation
7.2 Stability Analysis
7.3 Numerical Example
7.4 Notes and Comments
References
8 Robust Reliable Control for Impulsive Large-Scale Systems
8.1 Problem Formulation
8.2 Reliable Control
8.3 State Estimation
8.4 Notes and Comments
References
9 Switched Singularly Perturbed Systems with Time Delay
9.1 Problem Formulation
9.2 Stability Analysis
9.2.1 Linear Systems
9.2.2 Nonlinear Systems
9.3 Notes and Comments
References
10 Singularly Perturbed Impulsive-Switched Systems with Time Delay
10.1 Problem Formulation
10.2 Stability Analysis
10.2.1 Linear Systems
10.2.2 Nonlinear Systems
10.3 Notes and Comments
Reference
11 Stabilization and State Estimation via Sliding Mode Control
11.1 Problem Formulation
11.2 Slow Sliding Mode Control Design
11.2.1 Sliding Mode Control with Multiple Inputs
11.2.2 Reachability Analysis
11.3 Sliding Mode Luenberger Observer
11.4 Numerical Examples
11.5 Notes and Comments
References
12 Comparison Method and Stability of EPCA
12.1 Introduction
12.2 Problem Formulation
12.3 Comparison Method
12.4 Stability Analysis
12.5 Numerical Examples
12.6 Application
12.7 Notes and Comments References
13 Existence, Uniqueness and Stability of Stochastic EPCA
13.1 Existence and Uniqueness of Solutions
13.2 Comparison Method
13.3 Stability Analysis
13.4 Notes and Comments
References
