Nonlinear Control Systems
Analysis and Design
1. Auflage Mai 2003
376 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
Modern technological advances, bringing an ever increasing demand for better performance, coupled with the availability of low cost computer power, have lead control engineers to face problems of high complexity. More accurate, realistic, nonlinear models are now replacing linear approximations, once used as vehicles to approach the analysis of such problems. The result is that engineers must now abandon the view of the linear world and immerse themselves in the reality of nonlinear science. Assuming no previous background on the subject, this book provides a readable, peadagogical presentation of this difficult subject, taking the students from the very basics of Lyapunov theory to some of the latest research topics such as nonlinear observers and dissipative systems.
Provides complete coverage of both the Lyapunov and Input-Output stability theories, ina readable, concise manner.
* Supplies an introduction to the popular backstepping approach to nonlinear control design
* Gives a thorough discussion of the concept of input-to-state stability
* Includes a discussion of the fundamentals of feedback linearization and related results.
* Details complete coverage of the fundamentals of dissipative system's theory and its application in the so-called L2gain control prooblem, for the first time in an introductory level textbook.
* Contains a thorough discussion of nonlinear observers, a very important problem, not commonly encountered in textbooksat this level.
1.1 Linear Time-Invariant Systems.
1.2 Nonlinear Systems.
1.3 Equilibrium Points.
1.4 First-Order Autonomous Nonlinear Systems.
1.5 Second-Order Systems: Phase-Plane Analysis.
1.6 Phase-Plane Analysis of Linear Time-Invariant Systems.
1.7 Phase-Plane Analysis of Nonlinear Systems.
1.8 Higher-Order Systems.
1.9 Examples of Nonlinear Systems.
1.10 Exercises.
Mathematical Preliminaries.
2.1 Sets.
2.2 Metric Spaces.
2.3 Vector Spaces.
2.4 Matrices.
2.5 Basic Topology.
2.6 Sequences.
2.7 Functions.
2.8 Differentiability.
2.9 Lipschitz Continuity.
2.10 Contraction Mapping.
2.11 Solution of Differential Equations.
2.12 Exercises.
Lyapunov Stability I: Autonomous Systems.
3.1 Definitions.
3.2 Positive Definite Functions.
3.3 Stability Theorems.
3.4 Examples.
3.5 Asymptotic Stability in the Large.
3.6 Positive Definite Functions Revisited.
3.7 Construction of Lyapunov Functions.
3.8 The Invariance Principle.
3.9 Region of Attraction.
3.10 Analysis of Linear Time-Invariant Systems.
3.11 Instability.
3.12 Exercises.
Lyapunov Stability II: Nonautonomous Systems.
4.1 Definitions.
4.2 Positive Definite Functions.
4.3 Stability Theorems.
4.4 Proof of the Stability Theorems.
4.5 Analysis of Linear Time-Varying Systems.
4.6 Perturbation Analysis.
4.7 Converse Theorems.
4.8 Discrete-Time Systems.
4.9 Discretization.
4.10 Stability of Discrete-Time Systems.
4.11 Exercises.
Feedback Systems.
5.1 Basic Feedback Stabilization.
5.2 Integrator Backstepping.
5.3 Backstepping: More General Cases.
5.4 Examples.
5.5 Exercises.
Input-Output Stability.
6.1 Function Spaces.
6.2 Input-Output Stability.
6.3 Linear Time-Invariant Systems.
6.4 L_p Gains for LTI Systems.
6.5 Closed Loop Input-Output Stability.
6.6 The Small Gain Theorem.
6.7 Loop Transformations.
6.8 The Circle Criterion.
6.9 Exercises.
Input-to-State Stability.
7.1 Motivation.
7.2 Definitions.
7.3 Input-to-State Stability (ISS) Theorems.
7.4 Input-to-State Stability Revisited.
7.5 Cascade Connected Systems.
7.6 Exercises.
Passivity.
8.1 Power and Energy: Passive Systems.
8.2 Definitions.
8.3 Interconnections of Passivity Systems.
8.4 Stability of Feedback Interconnections.
8.5 Passivity of Linear Time-Invariant Systems.
8.6 Strictly Positive Real Rational Functions.
Exercises.
Dissipativity.
9.1 Dissipative Systems.
9.2 Differentiable Storage Functions.
9.3 QSR Dissipativity.
9.4 Examples.
9.5 Available Storage.
9.6 Algebraic Condition for Dissipativity.
9.7 Stability of Dissipative Systems.
9.8 Feedback Interconnections.
9.9 Nonlinear L_2 Gain.
9.10 Some Remarks about Control Design.
9.11 Nonlinear L_2-Gain Control.
9.12 Exercises.
Feedback Linearization.
10.1 Mathematical Tools.
10.2 Input-State Linearization.
10.3 Examples.
10.4 Conditions for Input-State Linearization.
10.5 Input-Output Linearization.
10.6 The Zero Dynamics.
10.7 Conditions for Input-Output Linearization.
10.8 Exercises.
Nonlinear Observers.
11.1 Observers for Linear Time-Invariant Systems.
11.2 Nonlinear Observability.
11.3 Observers with Linear Error Dynamics.
11.4 Lipschitz Systems.
11.5 Nonlinear Separation Principle.
Proofs.
Bibliography.
List of Figures.
Index.
