Robust Control Theory and Applications 1st Edition by Kang-Zhi Liu, Yu Yao ISBN 9781118754375 1118754379
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Product details:
ISBN 10: 1118754379
ISBN 13: 9781118754375
Author: Kang-Zhi Liu, Yu Yao
Comprehensive and up to date coverage of robust control theory and its application
• Presented in a well-planned and logical way
• Written by a respected leading author, with extensive experience in robust control
• Accompanying website provides solutions manual and other supplementary material
Table of contents:
1 Introduction
1.1 Engineering Background of Robust Control
1.2 Methodologies of Robust Control
1.3 A Brief History of Robust Control
2 Basics of Linear Algebra and Function Analysis
2.1 Trace, Determinant, Matrix Inverse, and Block Matrix
2.2 Elementary Linear Transformation of Matrix and Its Matrix Description
2.3 Linear Vector Space
2.4 Norm and Inner Product of Vector
2.5 Linear Subspace
2.6 Matrix and Linear Mapping
2.7 Eigenvalue and Eigenvector
2.8 Invariant Subspace
2.9 Pseudo-Inverse and Linear Matrix Equation
2.10 Quadratic Form and Positive Definite Matrix
2.11 Norm and Inner Product of Matrix
2.12 Singular Value and Singular Value Decomposition
2.13 Calculus of Vector and Matrix
2.14 Kronecker Product
2.15 Norm and Inner Product of Function
3 Basics of Convex Analysis and LMI
3.1 Convex Set and Convex Function
3.2 Introduction to LMI
3.3 Interior Point Method
4 Fundamentals of Linear System
4.1 Structural Properties of Dynamic System
4.2 Stability 100
4.3 Lyapunov Equation
4.4 Linear Fractional Transformation
5 System Performance
5.1 Test Signal
5.2 Steady-State Response
5.3 Transient Response
5.4 Comparison of Open-Loop and Closed-Loop Controls
6 Stabilization of Linear Systems
6.1 State Feedback
6.2 Observer
6.3 Combined System and Separation Principle
7 Parametrization of Stabilizing Controllers
7.1 Generalized Feedback Control System
7.2 Parametrization of Controllers
7.3 Youla Parametrization
7.4 Structure of Closed-Loop System
7.5 2-Degree-of-Freedom System
8 Relation between Time Domain and Frequency Domain Properties
8.1 Parseval’s Theorem
8.2 KYP Lemma
9 Algebraic Riccati Equation
9.1 Algorithm for Riccati Equation
9.2 Stabilizing Solution
9.3 Inner Function
10 Performance Limitation of Feedback Control
10.1 Preliminaries
10.2 Limitation on Achievable Closed-loop Transfer Function
10.3 Integral Relation
10.4 Limitation of Reference Tracking
11 Model Uncertainty
11.1 Model Uncertainty: Examples
11.2 Plant Set with Dynamic Uncertainty
11.3 Parametric System
11.4 Plant Set with Phase Information of Uncertainty
11.5 LPV Model and Nonlinear Systems
11.6 Robust Stability and Robust Performance
12 Robustness Analysis 1: Small-Gain Principle
12.1 Small-Gain Theorem
12.2 Robust Stability Criteria
12.3 Equivalence between H∞ Performance and Robust Stability
12.4 Analysis of Robust Performance
12.5 Stability Radius of Norm-Bounded Parametric Systems
13 Robustness Analysis 2: Lyapunov Method
13.1 Overview of Lyapunov Stability Theory
13.2 Quadratic Stability
13.3 Lur’e System
13.4 Passive Systems
14 Robustness Analysis 3: IQC Approach
14.1 Concept of IQC
14.2 IQC Theorem
14.3 Applications of IQC
14.4 Proof of IQC Theorem
Notes and References
15 H2 Control
15.1 H2 Norm of Transfer Function
15.2 H2 Control Problem
15.3 Solution to Nonsingular H2 Control Problem
15.4 Proof of Nonsingular Solution
15.5 Singular H2 Control
15.6 Case Study: H2 Control of an RTP System
16 H∞ Control
16.1 Control Problem and H∞ Norm
16.2 H∞ Control Problem
16.3 LMI Solution 1: Variable Elimination
16.4 LMI Solution 2: Variable Change
16.5 Design of Generalized Plant and Weighting Function
16.6 Case Study
16.7 Scaled H∞ Control
17 μ Synthesis
17.1 Introduction to μ
17.2 Definition of μ and Its Implication
17.3 Properties of μ
17.4 Condition for Robust H∞ Performance
17.5 D–K Iteration Design
17.6 Case Study
18 Robust Control of Parametric Systems
18.1 Quadratic Stabilization of Polytopic Systems x
18.2 Quadratic Stabilization of Norm-Bounded Parametric Systems
18.3 Robust H∞ Control Design of Polytopic Systems
18.4 Robust H∞ Control Design of Norm-Bounded Parametric Systems
19 Regional Pole Placement
19.1 Convex Region and Its Characterizationx
19.2 Condition for Regional Pole Placement x
19.3 Composite LMI Region 39219.4 Feedback Controller Design x
19.5 Analysis of Robust Pole Placement x
19.6 Robust Design of Regional Pole Placement406x
20 Gain-Scheduled Control
20.1 General Structurex
20.2 LFT-Type Parametric Model
20.3 Case Study: Stabilization of a Unicycle Robot
20.4 Affine LPV Model
20.5 Case Study: Transient Stabilization of a Power System
21 Positive Real Method
21.1 Structure of Uncertain Closed-Loop Systemx
21.2 Robust Stabilization Based on Strongly Positive Realness
21.3 Robust Stabilization Based on Strictly Positive Realness
21.4 Robust Performance Design for Systems with Positive Real Uncertainty
21.5 Case Study
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Kang-Zhi Liu,Yu Yao,Robust Control,Theory and Applications