Author | Krasnosel'skiว, Mark A. author |
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Title | Systems with Hysteresis [electronic resource] / by Mark A. Krasnosel'skiว, Aleksei V. Pokrovskiว |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1989 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61302-9 |
Descript | XVIII, 410 p. online resource |
1 Static Hysteron -- 1. Short-memory transducer -- 2. Generalized play -- 3. Hysteron -- 4. Canonical representation of hysteron and proof of Theorem 3.2 -- 5. Distances -- 6. Various input spaces -- 2 Identification Theorem -- 7. Identification problem -- 8. Proof of Theorem 7.1 -- 9. ? - identiflability -- 10. Approximate construction of hysteron -- 3 Vibro-Correct Differential Equations and Variable Hysterons -- 11. Necessary condition of vibro-correctness -- 12. Sufficient condition of vibro-correctness -- 13. Vibro-solutions -- 14. Equations with constraints -- 15. Variable hysteron -- 4 Multidimensional Hysterons -- 16. Multidimensional play and stop defined on smooth inputs -- 17. Strictly convex characteristics -- 18. Polyhedral characteristics -- 19. Arbitrary convex characteristics -- 20. Inputs with summable derivatives -- 21. Vibro-correct equations with vector input -- 22. Equations with vector inputs and smooth constraints -- 5 Discontinuous Nonlinearities -- 23. Static elements -- 24. Elements with monotone characteristics -- 25. Elements with multi-valued characteristics -- 26. Closures of static element -- 27. Weak closures and convexification procedure -- 28. Relay -- 6 Self-Magnetization Phenomenon -- 29. Madelung's hysterons -- 30. Proofs of Theorems 29.1 and 29.2 -- 31. Response to small perturbations of the input -- 32. Closure modulo sets of Wiener measure zero -- 7 Complex Hysteresis Nonlinearities -- 33. Parallel connections and bundles of hysterons -- 34. Sequential connections of hysterons -- 35. Ishlinskii's material -- 36. Properties of Ishlinskii's transducer -- 37. Finite systems of relays -- 38. Continual systems of relays -- 39. Rheological models -- Bibliographic comments -- References