Stability of Nonlinear Control Systems (Mathematics in Science and Engineering)

✍ Scribed by Solomon Lefschetz

• Publisher: Academic Press
• Year: 1965
• Tongue: English
• Leaves: 163
• Category: Library

✦ Table of Contents

Front Cover
Stability of Nonlinear Control Systems
Copyright Page
Contents
Preface
Special Abridged Notations
Introduction
Chapter One. Introductory Treatment of Dimensions One and Two
1. The Characteristic Function
2. Systems of Dimension Unity. Direct Control
3. System of Dimension Unity. Indirect Control
4. System of Order Two
Chapter Two. Indirect Controls
1. Vectors and Matrices
2. Indirect Control. General Type
3. Comparison with a Recent Result of Yacubovich
4. On the Utilization of Certain Complex Coordinate Systems
5. Special Cases
Chapter Three. Indirect Controls (Continued)
1. Invariance under Change of Coordinates
2. Reduction of the Number of Conditions on the Control Parameters
3. Lurie's Method and a Variant
4. Application to Systems of Order Two
Chapter Four. Direct Controls. Linearization Multiple Feedback
1. Direct Control: General Case
2. Direct Control, Standard Example
3. Reduction of an Indirect Control to a Special Direct Control
4. Linearization of Direct Controls
5. Linearization of Indirect Controls
6. Direct Control with Matrices B or C of Rank < n
7. Direct Controls with Matrices B, C, of Rank n – 1
8. Direct Control Whose Matrix A Has Zero as a Characteristic Root
9. Direct Control Whose Matrix Has a Pair of Conjugate Pure Imaginary Characteristic Roots
10. Multiple Feedbacks
Chapter Five. Systems Represented by a Set of Equations of Higher Order
1. Generalities
2. A Digression on Linear Systems
3. Indirect Control
4. Indirect Control: An Example
5. Direct Control
Chapter Six. Discontinuous Characteristics
1. Continuous Approximation of Discontinuous Characteristics
2. Direct Discussion of Discontinuities
3. Some Examples
4. Special Switching Lines
5. Multiple Feedback Switching Line
6. Complementary Remarks
Chapter Seven. Some Recent Results of V. M. Popov
1. Generalities. The Theorems of Popov
2. Preliminary Properties
3. Proof of Popov’s First Theorem
4. The Generalized Liapunov Function of Popov
5. Proop of Popov’s Second Theorem
6. Comparisons
7. On the Function G (z) as Transfer Function
8. Direct Control
9. Conclusion
Chapter Eight. Some Further Recent Contributions
1. Controllability and Observability
2. Reduction of the System to One with a Completely Controllable Pair ( A, b) and Completely Observable Pair (c’, A )
3. A Special Form for Systems with Completely Controllable Pair ( A, b )
4. Main Lemma
5. Liapunov–Popov Function and Popov Inequality
6. Fundamental Theorem
7. A Recent Result of Morozan
8. Return to the Standard Example
9. Direct Control


Chapter Nine. Miscellaneous Complements
1. The Jordan Normal Form for Real or Complex Matrices
2. On a Determinantal Relation
3. On Liapunov’s Matrix Equation
4. Liapunov and Stability
Appendix A: An Application of Multiple Feedback Control
Appendix B: An Example from the Theory of Nuclear Power Reactors
Bibliography
Index