Frequency Domain Criteria for Absolute Stability

1. Front Matter

   Pages 1-8

   PDF

2. A Historical Survey

   • Dmitry Altshuller

   Pages 1-24

3. Foundations

   • Dmitry Altshuller

   Pages 25-41

4. Stability Multipliers

   • Dmitry Altshuller

   Pages 43-80

5. Time-Periodic Systems

   • Dmitry Altshuller

   Pages 81-115

6. Back Matter

   Pages 0--1

   PDF

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.

• Automatic Control
• Control Theory
• Frequency-domain Methods
• Gradient Nonlinearities
• Monotone Nonlinearities
• Quasimonotone Nonlinearities
• System Stability

• Riverside, USA

  Dmitry Altshuller

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