Page 14 -

xii CONTENTS

Linear Vector Spaces 39
Norms of Signals and Systems 40
Inner Products 48
Matrix Properties 48
2.6 Stability Theory 51
2.7 Lyapunov Stability Theorems 67
Functions Of Class K 67
Lyapunov Theorems 69
The Autonomous Case 72
2.8 Input/Output Stability 80
2.9 Advanced Stability Results 82
Passive Systems 82
Positive-Real Systems 84
Lure’s Problem 85
The MKY Lemma 86
2.10 Useful Theorems and Lemmas 88
Small-Gain Theorem 88
Total Stability Theorem 89
2.11 Linear Controller Design 93
2.12 Summary and Notes 101
References 103

3 Robot Dynamics 107
3.1 Introduction 107
3.2 Lagrange-Euler Dynamics 108
Force, Inertia, and Energy 108
Lagrange’s Equations of Motion 111
Derivation of Manipulator Dynamics 119
3.3 Structure and Properties of the Robot Equation 125
Properties of the Inertia Matrix 126
Properties of the Coriolis/Centripetal Term 127
Properties of the Gravity, Friction,
and Disturbance 134
Linearity in the Parameters 136
Passivity and Conservation of Energy 141
3.4 State-Variable Representations and Feedback Linearization 142
Hamiltonian Formulation 143
Position/Velocity Formulations 145
Feedback Linearization 145
3.5 Cartesian and Other Dynamics 148
Cartesian Arm Dynamics 148

Copyright © 2004 by Marcel Dekker, Inc.