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" Systems with delays : "
A.V. Kim and A.V. Ivanov
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BL
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| Record Number
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662641
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dltt
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| Main Entry
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Kim, A. V.
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| Title & Author
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Systems with delays : : analysis, control, and computations /\ A.V. Kim and A.V. Ivanov
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| Page. NO
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1 online resource
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| ISBN
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9781118998526 (Adobe PDF)
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: 1118998529 (Adobe PDF)
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: 9781118998540 (ePub)
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: 1118998545 (ePub)
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9781119117582 (cloth)
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: 9781119117728
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: 1119117720
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: 9781119117841
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: 1119117844
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: 1119117585
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: 9781119117582
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: 9781119117735
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: 1119117739
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Linear time-delay systems -- Introduction -- Linear systems with delays -- Wind tunnel model -- Combustion stability in liquid propellant rocket motors -- Conditional representation of differential equations -- Conditional representation of ODE and PDE -- Conditional representation of DDE -- Initial Value Problem. Notion of solution -- Initial conditions (initial state) -- Notion of a solution -- Functional spaces -- Space C[-τ,0] -- Space Q[-τ,0] -- Space Q[-τ,0) -- Space H = Rη x Q[-τ,0) -- Phase space H. State of time-delay system -- Solution representation -- Time-varying systems with delays -- Time-invariant systems with delays -- Characteristic equation and solution expansion into a series -- Characteristic equation and eigenvalues -- Expansion of solution into a series on elementary solutions -- Stability theory -- Introduction -- Statement of the stability problem -- Eigenvalues criteria of asymptotic stability -- Stability via the fundamental matrix -- Stability with respect to a class of functions -- Lyapunov-Krasovskii functionals -- Structure of Lyapunov-Krasovskii quadratic functionals -- Elementary functionals and their properties -- Total derivative of functionals with respect to systems with delays -- Positiveness of functionals -- Definitions -- Sufficient conditions of positiveness -- Positiveness of functionals -- Stability via Lyapunov-Krasovskii functionals -- Stability conditions in the norm H -- Stability conditions in the norm -- Converse theorem -- Examples -- Coefficient conditions of stability -- Linear system with discrete delay -- Linear system with distributed delays -- Linear quadratic control -- Introduction -- Statement of the problem -- Explicit solutions of generalized Riccati equations -- Variant 1 -- Variant 2 -- Variant 3 -- Solution of Exponential Matrix Equation -- Stationary solution method -- Gradient methods -- Design procedure -- Variants 1 and 2 -- Variant 3 -- Design case studies -- Example 1 -- Example 2 -- Example 3 -- Example 4 -- Example 5: Wind tunnel model -- Example 6: Combustion stability in liquid propellant rocketmotors -- Numerical methods -- Introduction -- Elementary one-step methods -- Euler'smethod -- Implicit methods (extrapolation) -- Improved Euler'smethod -- Runge-Kutta-like methods -- Interpolation and extrapolation of the model pre-history -- Interpolational operators -- Extrapolational operators -- Interpolation-Extrapolation operator -- Explicit Runge-Kutta-like methods -- Approximation orders of ERK-like methods -- Automatic step size control -- Richardson extrapolation -- Automatic step size control -- Embedded formulas -- Appendix -- i-Smooth calculus of functionals -- Invariant derivative of functionals -- Examples -- Derivation of generalized Riccati equations -- Explicit solutions of GREs (proofs of theorems) -- Proof of Theorem 3.2 -- Proof of Theorem 3.3 -- Proof of Theorem 3.4 -- Proof of Theorem 1.1. (Solution representation)
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| Subject
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Delay differential equations.
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Linear systems.
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Derivatives (Mathematics)
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| Dewey Classification
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515/.35
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| LC Classification
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QA372
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| Added Entry
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Ivanov, A. V.
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Ohio Library and Information Network.
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