| Description |
1 online resource (xv, 334 pages) : illustrations |
| Series |
Series on stability, vibration, and control of systems. Series A ; v. 14 |
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Series on stability, vibration, and control of systems. Series A ; v. 14.
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| Contents |
1. Foundations of theory of differential equations with discontinuous right-hand sides. 1.1. Notion of solution to differential equation with discontinuous right-hand side. 1.2. Systems of differential equations with multiple-valued right-hand sides (differential inclusions). 1.3. Dichotomy and stability -- 2. Auxiliary algebraic statements on solutions of matrix inequalities of a special type. 2.1. Algebraic problems that occur when finding conditions for the existence of Lyapunov functions from some multiparameter functional class. Circle criterion. Popov criterion. 2.2. Relevant algebraic statements -- 3. Dichotomy and stability of nonlinear systems with multiple equilibria. 3.1. Systems with piecewise single-valued nonlinearities. 3.2. Systems with monotone piecewise single-valued nonlinearities. 3.3. Systems with gradient nonlinearities -- 4. Stability of equilibria sets of pendulum-like systems. 4.1. Formulation of the stability problem for equilibrium sets of pendulum-like systems. 4.2. The method of periodic Lyapunov functions. 4.3. An analogue of the circle criterion for pendulum-like systems. 4.4. The method of non-local reduction. 4.5. Necessary conditions for gradient-like behavior of pendulum-like systems. 4.6. Stability of the dynamical systems describing the synchronous machines -- 5. Appendix. Proofs of the theorems of chapter 2. 5.1. Proofs of theorems on controllability, observability, irreducibility, and of lemmas 2.4 and 2.7. 5.2. Proof of theorem 2.13 (nonsingular Case). Theorem on solutions of Lur'e equation (algebraic Riccati equation). 5.3. Proof of theorem 2.13 (completion) and lemma 5.1. 5.4. Proofs of theorems 2.12 and 2.14 (singular Case). 5.5. Proofs of theorems 2.17-2.19 on losslessness of S-procedure |
| Summary |
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines |
| Bibliography |
Includes bibliographical references (pages 323-332) and index |
| Notes |
Print version record |
| Subject |
Control theory.
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Nonlinear control theory.
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Set theory.
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System analysis
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Differential equations, Nonlinear.
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Engineering mathematics.
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Engineering systems.
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Systems Analysis
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systems analysis.
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TECHNOLOGY & ENGINEERING -- Automation.
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TECHNOLOGY & ENGINEERING -- Robotics.
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Control theory
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Differential equations, Nonlinear
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Engineering mathematics
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Engineering systems
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Nonlinear control theory
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Set theory
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System analysis
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Controleleer.
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Verzamelingen (wiskunde)
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Systeemtheorie.
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Systeemanalyse.
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| Form |
Electronic book
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| Author |
Leonov, G. A. (Gennadiĭ Alekseevich)
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Gelig, Arkadiĭ Khaĭmovich
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| ISBN |
9789812794239 |
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9812794239 |
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