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
