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混合系統理論確定系統與隨機系統 版權信息
- ISBN：9787040506150
- 條形碼：9787040506150 ; 978-7-04-050615-0
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
混合系統理論確定系統與隨機系統 內容簡介
本書介紹了確定性和隨機混合系統的理論。混合系統是一個橫跨應用數學、控制科學和計算機科學等學科的交叉研究領域。在此類系統中，若干個連續過程與不同層次的自動化設備相互作用。這些自動化裝置起著監督、管理和決策作用，從而構成多個離散事件過程，這些集若干連續過程與若干離散過程為一體的大型反應系統即構成一個混合系統。混合系統的理論為大型反應系統提供了一個很好的數學模型，它是一個非常有價值的建模工具，可用于描述廣泛的現實世界的應用。本書介紹了多個 Lyapunov或Razumikhin–Lyapunov函數方法，討論了確定性和隨機混合系統領域的極新發展。本書還論述了系統的穩定性、穩定化、可靠控制、輸入-狀態穩定性(ISS) 穩定化、狀態估計和大規模奇異攝動系統的穩定性等性質。
混合系統理論確定系統與隨機系統 目錄
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
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