Frequency domain criteria for absolute stability : a delay-integral-quadratic constraints approach

✍ Scribed by Dmitry Altshuller

• Publisher: Springer
• Year: 2013
• Tongue: English
• Leaves: 146
• Series: Lecture notes in control and information sciences, 432
• Category: Library

✦ Synopsis

Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity. The results are presented in the frequency domain - the form in which they naturally tend to arise. In some cases, the frequency-domain criteria can be converted into computationally tractable linear matrix inequalities but in others, especially those with a certain geometric interpretation, inferences concerning stability can be made directly from the frequency-domain inequalities. The book is intended for applied mathematicians and control systems theorists. It can also be of considerable use to mathematically-minded engineers working with nonlinear systems. Read more... A Historical Survey -- Foundations -- Stability Multipliers -- Time-Periodic Systems

✦ Table of Contents

Cover......Page 1
Front matter......Page 2
Introduction......Page 10
Resolving Equations and Matrix Inequalities......Page 12
The Popov Criterion and Its Modifications......Page 14
Kalman-Yakubovich Lemma and the Circle Criterion......Page 19
Subsequent Development......Page 21
The Problem of Input-Output Stability......Page 24
The Method of Integral-Quadratic Constraints......Page 26
Flying Vehicle......Page 27
Hydraulic Regulator......Page 30
Modern Formulation of the Absolute Stability Problem......Page 34
Quadratic Criterion......Page 36
Two Integral Inequalities......Page 41
Proof of Lemma 2.3......Page 44
Proof of Lemma 2.7......Page 47
General Form for Stability Multipliers for SISO Systems......Page 51
Multipliers for Stationary SISO Systems......Page 58
Zames-Falb Multipliers......Page 59
Case of an Absolutely Continuous Kernel: Popov Criterion......Page 63
Case of a Differentiable Nonlinearity: Yakubovich Criterion......Page 67
Stability Multipliers for MIMO Systems......Page 70
Geometric Interpretation of Stability Multipliers......Page 77
Numerical Implementation of Stability Multipliers......Page 80
Proof of Lemma 3.1......Page 81
Proof of Lemma 3.2......Page 85
Verification of Minimal Stability......Page 87
Frequency Condition for Time Periodic Systems......Page 89
SISO Systems with Monotone Lipschitz Nonlinearities......Page 90
Stability Multipliers......Page 91
Lipatov Plots and Examples......Page 94
MIMO Systems with Gradient Nonlinearities......Page 98
SISO Systems with Quasimonotone Nonlinearities......Page 102
Quasimonotone Nonlinearities in the Sense of Barabanov......Page 103
The Second Type of Quasimonotone Nonlinearities......Page 108
Case When P(t) Is a Column Vector......Page 112
Case When P(t) Is a Nonsingular Square Matrix......Page 115
Yakubovich Criterion and Its MIMO Analogue......Page 118
SISO Systems with Parametric Class of Nonlinearities......Page 121
Concluding Remarks......Page 123
Back matter......Page 124