Stability and Stabilization: Fossard, A. J.; Normand-Cyrot, D. : 9780412600005: Book: Technology: eCampus.com

Nonlinear Systems is divided into three volumes. The first deals with modeling and estimation, the second with stability and stabilization and the third with control. This three-volume set provides the most comprehensive and detailed reference available on nonlinear systems. Written by a group of leading experts in the field, drawn from industry, government and academic institutions, it provides a solid theoretical basis on nonlinear control methods as well as practical examples and advice for engineers, teachers and researchers working with nonlinear systems. Each book focuses on the applicability of the concepts introduced and keeps the level of mathematics to a minimum. Simulations and industrial examples drawn from aerospace as well as mechanical, electrical and chemical engineering are given throughout.

Preface

(4)

Contents

(8)

List of contributors

xvii

Chapter 1. Asymptotic behavior of uncontrolled dynamical systems

(40)

J. LEVINE

1.1 Introduction

(2)

1.2 Recalls on differential equations

(7)

1.3 Stability of singular points and orbits

(6)

1.4 Local equivalence to a linear vector field

(14)

1.5 Extension to time-varying systems

(5)

1.6 Brief introduction to bifurcation theory

(1)

1.7 Concluding remarks: the role of controls

(1)

1.8 Bibliography

(4)

Chapter 2. Stability, stabilization, regulation using vector norms

(46)

P. BORNE

J. P. RICHARD

N. E. RADHY

2.1 Introduction

(6)

2.2 Definitions, notations and behavior examples

(4)

2.3 Use of vector norms: comparison systems

(5)

2.4 Theorems on stability

(11)

2.5 Determination of state feedbacks under constraints

(7)

2.6 Discrete systems

(7)

2.7 Stabilization of discrete systems under state constraints

(3)

2.8 Conclusion

(1)

2.9 Bibliography

(2)

Chapter 3. Stabilization of "linear with varying coefficients" systems

(22)

D. MEIZEL

3.1 The application field of the method

(1)

3.2 The studied problems

(2)

3.3 Initial statement of studied process models

(3)

3.4 Nonlinear stability analysis for controller parameter design

(5)

3.5 Nondifferentiable optimization

102

(3)

3.6 The design method

105

(2)

3.7 Example

107

(3)

3.8 Conclusion

110

(1)

3.9 Bibliography

110

(3)

Chapter 4. Stability and control of saturated linear systems

113

(86)

C. BURGAT

S. TARBOURIECH

4.1 Preliminary definitions

113

(12)

4.2 Specificities of saturated state feedback systems

125

(8)

4.3 Stability of the saturated regulator - problem position

133

(2)

4.4 Global(semi-global) stability of the regulator

135

(35)

4.5 Local stability of saturated regulators

170

(12)

4.6 Dual-mode control

182

(7)

4.7 State constraints - bilinear systems

189

(3)

4.8 Bibliography

192

(7)

Appendix A. Some differential geometric recalls

199

(10)

A.1 Differentiable manifold, diffemorphism

199

(1)

A.2 Tangent space, vector field, Lie derivative

200

(2)

A.3 Lie bracket

202

(2)

A.4 Distribution of vector fields

204

(1)

A.5 Frobenius theorem

204

(1)

A.6 Application to the computation of solutions of first-order partial differential equations

205

(1)

A.7 More on differential forms, duality

206

(2)

A.8 Bibliography

208

(1)

Appendix B. Vector norms - overvaluing matrices

209

(8)

B.1 Vector norms

209

(1)

B.2 Properties of the pseudo-overvaluing matrices(continuous case)

210

(1)

B.3 General determination of the NHOS (continuous case)

211

(3)

B.4 Definition of the overvaluing matrices (discrete case

214

(3)

Appendix C. Positives matrices - norms

217

(4)

C.1 Introduction

217

(1)

C.2 Positive definite matrices

217

(1)

C.3 Norms

217

(4)

Appendix D. M-matrices

221

(4)

D.1 Introduction

221

(1)

D.2 M-matrices

221

(1)

D.3 Bibliography

222

(3)

Appendix E. On the matrices equations XA + XBX = CX and AX + XB = C

225

(16)

E.1 Introduction

225

(1)

E.2 On the equation XA + XBX = CX

225

(2)

E.3 On the equation AX + XB = C

227

(11)

E.4 Bibliography

238

(3)

Index

241


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