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E-grāmata: Lectures in Feedback Design for Multivariable Systems

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Lectures in Feedback Design for Multivariable SystemsPalielināt
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This book focuses on methods that relate, in one form or another, to the “small-gain theorem”. It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and   more advanced topics.

Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory. In order to deepen readers’ understanding, simpler single-input–single-output systems generally precede treatment of more complex multi-input–multi-output (MIMO) systems and linear systems precede nonlinear systems. This approach is used throughout, including in the final chapters, which explain the latest advanced ideas governing the stabilization, regulation, and tracking of nonlinear MIMO systems. Two major design problems are considered, both in the presence of model uncertainties: asymptotic stabilization with a “guaranteed region of attraction” of a given equilibrium point and asymptotic rejection of the effect of exogenous (disturbance) inputs on selected regulated outputs.

Much of the introductory instructional material in this book has been developed for teaching students, while the final coverage of nonlinear MIMO systems offers readers a first coordinated treatment of completely novel results. The worked examples presented provide the instructor with ready-to-use material to help students to understand the mathematical theory.

Readers should be familiar with the fundamentals of linear-systems and control theory. This book is a valuable resource for students following postgraduate programs in systems and control, as well as engineers working on the control of robotic, mechatronic and power systems.


Recenzijas

This book by Alberto Isidori is devoted to the problem of output feedback stabilization. Although the book is directed to (current and future) control engineers rather than mathematicians, it is written with mathematical rigor. It contains precise definitions, clearly stated theorems and precise proofs. There are many examples with detailed computations, which help the reader understand long theoretical discussions. (Zbigniew Bartosiewicz, Mathematical Reviews, April, 2018)

1 An Overview
1(20)
1.1 Introduction
1(1)
1.2 Robust Stabilization of Linear Systems
2(4)
1.3 Regulation and Tracking in Linear Systems
6(1)
1.4 From Regulation to Consensus
7(1)
1.5 Feedback Stabilization and State Observers for Nonlinear Systems
8(4)
1.6 Robust Stabilization of Nonlinear Systems
12(1)
1.7 Multi-input Multi-output Nonlinear Systems
13(4)
1.8 Regulation and Tracking in Nonlinear Systems
17(4)
Part I Linear Systems
2 Stabilization of Minimum-Phase Linear Systems
21(22)
2.1 Normal Form and System Zeroes
21(7)
2.2 The Hypothesis of Minimum-Phase
28(2)
2.3 The Case of Relative Degree 1
30(2)
2.4 The Case of Higher Relative Degree: Partial State Feedback
32(5)
2.5 The Case of Higher Relative Degree: Output Feedback
37(6)
References
42(1)
3 The Small-Gain Theorem for Linear Systems and Its Applications to Robust Stability
43(40)
3.1 The 2 Gain of a Stable Linear System
43(4)
3.2 An LMI Characterization of the 2 Gain
47(2)
3.3 The H∞ Norm of a Transfer Function
49(3)
3.4 The Bounded Real Lemma
52(5)
3.5 Small-Gain Theorem and Robust Stability
57(14)
3.6 The Coupled LMIs Approach to the Problem of γ-Suboptimal H∞ Feedback Design
71(12)
References
81(2)
4 Regulation and Tracking in Linear Systems
83(52)
4.1 The Problem of Asymptotic Tracking and Disturbance Rejection
83(2)
4.2 The Case of Full Information and Francis' Equations
85(7)
4.3 The Case of Measurement Feedback: Steady-State Analysis
92(3)
4.4 The Case of Measurement Feedback: Construction of a Controller
95(7)
4.5 Robust Output Regulation
102(2)
4.6 The Special Case in Which m = p and pr = 0
104(9)
4.7 The Case of SISO Systems
113(4)
4.8 Internal Model Adaptation
117(10)
4.9 Robust Regulation via H∞ Methods
127(8)
References
132(3)
5 Coordination and Consensus of Linear Systems
135(32)
5.1 Control of a Network of Systems
135(2)
5.2 Communication Graphs
137(2)
5.3 Leader-Follower Coordination
139(8)
5.4 Consensus in a Homogeneous Network: Preliminaries
147(6)
5.5 Consensus in a Homogeneous Network: Design
153(4)
5.6 Consensus in a Heterogeneous Network
157(10)
References
162(5)
Part II Nonlinear Systems
6 Stabilization of Nonlinear Systems via State Feedback
167(34)
6.1 Relative Degree and Local Normal Forms
167(6)
6.2 Global Normal Forms
173(3)
6.3 The Zero Dynamics
176(3)
6.4 Stabilization via Full State Feedback
179(6)
6.5 Stabilization via Partial State Feedback
185(9)
6.6 Examples and Counterexamples
194(7)
References
198(3)
7 Nonlinear Observers and Separation Principle
201(32)
7.1 The Observability Canonical Form
201(7)
7.2 The Case of Input-Affine Systems
208(3)
7.3 High-Gain Nonlinear Observers
211(4)
7.4 The Gains of the Nonlinear Observer
215(6)
7.5 A Nonlinear Separation Principle
221(6)
7.6 Examples
227(6)
References
230(3)
8 The Small-Gain Theorem for Nonlinear Systems and Its Applications to Robust Stability
233(18)
8.1 The Small-Gain Theorem for Input-to-State Stable Systems
233(6)
8.2 Gain Assignment
239(4)
8.3 An Application to Robust Stability
243(8)
References
249(2)
9 The Structure of Multivariable Nonlinear Systems
251(42)
9.1 Preliminaries
251(1)
9.2 The Basic Inversion Algorithm
252(11)
9.3 An Underlying Recursive Structure of the Derivatives of the Output
263(3)
9.4 Partial and Full Normal Forms
266(14)
9.5 The Case of Input-Output Linearizable Systems
280(8)
9.6 The Special Case of Systems Having Vector Relative Degree
288(5)
References
291(2)
10 Stabilization of Multivariable Nonlinear Systems: Part I
293(26)
10.1 The Hypothesis of Strong Minimum-Phase
293(2)
10.2 Systems Having Vector Relative Degree: Stabilization via Full State Feedback
295(2)
10.3 A Robust "Observer"
297(8)
10.4 Convergence Analysis
305(14)
References
316(3)
11 Stabilization of Multivariable Nonlinear Systems: Part II
319(22)
11.1 Handling Invertible Systems that Are Input-Output Linearizable
319(7)
11.2 Stabilization by Partial-State Feedback
326(2)
11.3 Stabilization via Dynamic Output Feedback
328(5)
11.4 Handling More General Classes of Invertible Systems
333(8)
References
340(1)
12 Regulation and Tracking in Nonlinear Systems
341(24)
12.1 Preliminaries
341(2)
12.2 Steady-State Analysis
343(4)
12.3 The Case of SISO Systems
347(5)
12.4 The Design of an Internal Model
352(7)
12.5 Consensus in a Network of Nonlinear Systems
359(6)
References
363(2)
Appendix A Background Material in Linear Systems Theory 365(20)
Appendix B Stability and Asymptotic Behavior of Nonlinear Systems 385(26)
Index 411
Alberto Isidori obtained his degree in Electrical Engineering (EE) from the University of Rome in 1965. From 1975 to 2012, he was Professor of Automatic Control there and is now Professor Emeritus. His research interests are primarily in analysis and design of nonlinear control systems. He is the author of several books, such as the highly cited "Nonlinear Control Systems". He is the recipient of various prestigious awards,   including the IFAC Giorgio Quazza Medal (in 1996), the Ktesibios Award (in 2000), the Bode Lecture Award from the IEEE Control Systems Society (in 2001), an Honorary Doctorate from KTH of Sweden (in 2009), the  Galileo Galilei Award from the Rotary Clubs of Italy (in 2009), and the IEEE Control Systems Award (in 2012). In 2012 he was also elected corresponding member of the Accademia Nazionale dei Lincei. He is the recipient of awards for best papers published in the IEEE Transactions on Automatic Control and in Automatica, twice for each journal. In1986 he was elected a Fellow of IEEE, and in 2005 he was elected a Fellow of IFAC. He was the President of IFAC in the triennium 20082011.
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