| Description |
1 online resource (xv, 334 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| 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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| Bibliography |
Includes bibliographical references (pages 323-332) and index. |
| 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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Control theory.
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Control theory. |
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Nonlinear control theory.
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Nonlinear control theory. |
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Set theory.
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Set theory. |
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System analysis.
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System analysis. |
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Differential equations, Nonlinear.
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Differential equations, Nonlinear. |
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Engineering mathematics.
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Engineering mathematics. |
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Engineering systems.
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Engineering systems. |
| Genre/Form |
Electronic books.
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| Added Author |
Leonov, G. A. (Gennadiĭ Alekseevich)
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Gelig, Arkadiĭ Khaĭmovich.
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| Other Form: |
Print version: I͡Akubovich, V.A. (Vladimir Andreevich). Stability of stationary sets in control systems with discontinuous nonlinearities. River Edge, NJ : World Scientific, ©2004 9812387196 9789812387196 (DLC) 2005297772 (OCoLC)55875661 |
| ISBN |
9789812794239 (electronic book) |
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9812794239 (electronic book) |
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9812387196 |
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9789812387196 |
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