Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

/pdf/stability-of-time-delay-systems-5d2qjgdknf.pdf

Stability of Time-Delay Systems

The structural properties of oxygen-deficient ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ have been determined by neutron powder diffraction for 0.07l\ensuremath{\delta}l0.91. The samples were produced by quenching into liquid nitrogen from controlled oxygen partial pressures at 520 \ifmmode^\circ\else\textdegree\fi{}C, and they exhibit a clearly defined ``plateau'' behavior of ${T}_{c}$ versus \ensuremath{\delta}. Superconductivity disappears at the orthorhombic-to-tetragonal transition that occurs near \ensuremath{\delta}=0.65. Structural parameters, including the copper-oxygen bond lengths, vary smoothly with \ensuremath{\delta} within each phase but exhibit different behavior in the superconducting and nonsuperconducting phases. These observations are consistent with a model in which superconducting behavior is controlled by charge transfer between the conducting two-dimensional ${\mathrm{CuO}}_{2}$ planes and the ${\mathrm{CuO}}_{\mathrm{x}}$ chains, which act as reservoirs of charge.

Structural properties of oxygen-deficient YBa2Cu3O7- delta.

We report the characterization of series of oxygen deficient Ba2YCu3Ox samples for 7 ≥ x ≥ 6 prepared by Zr gettered annealing at 440°C. Measurements include complete crystal structure analysis at 5 K by powder neutron diffraction, electron microscopy study of the oxygen ordering, and magnetic measurements of the superconducting transitions, with particular attention to the transition widths. The results show for the first time that the 90 K and 60 K plateaus in Tc as a function of oxygen stoichiometry are associated with plateaus in the effective valence of the plane coppers. We also correlate the disappearance of superconductivity for x

Structural anomalies, oxygen ordering and superconductivity in oxygen deficient Ba2YCu3Ox

Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator

We study the nonlinear oscillator ẍ + δẋ — βx + αx 3 = f cos (ω t ) (A) from a qualitative viewpoint, concentrating on the bifurcational behaviour occurring as f > 0 increases for α, β, δ, ω to fixed > 0. In particular, we study the global nature of attracting motions arising as a result of bifurcations. We find that, for small and for large f , the behaviour is much as expected and that the conventional Krylov-Bogoliubov averaging theorem yields acceptable results. However, for a wide range of moderate f extremely complicated non-periodic motions arise. Such motions are called strange attractors or chaotic oscillations and have been detected in previous studies of autonomous o.d.es of dimension > 3. In the present case they are intimately connected with homoclinic orbits arising as a result of global bifurcations. We use recent results of Mel’nikov and others to prove that such motions occur in (A) and we study their structure by means of the Poincare map associated with (A). Using analogue and digital computer simulations, we provide a fairly complete characterization of the strange attractor arising for moderate f . This ergodic motion arises naturally from the deterministic differential equation (A).

A nonlinear oscillator with a strange attractor

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.

Randomly transitional phenomena in the system governed by Duffing's equation

/pdf/some-problems-in-the-theory-of-nonlinear-oscillations-1mclq7qyx5.pdf

Some problems in the theory of nonlinear oscillations

Randomly Transitional Phenomena in the System Governed by Duffing's Equation

This paper deals with chaotically transitional phenomena which occur In the forced negative-resistance oscillator. Experimental studies using analog and digital computers have been carried out. The difference between the almost periodic oscillations and the chaotically transitional processes is clarified. Various strange attractors representing chaotically transitional processes and their average power spectra are given. They are discussed in detail and compared with the results obtained in the forced oscillatory systems.

Chaotically transitional phenomena in the forced negative-resistance oscillator

Explosion of strange attractors exhibited by duffing's equation

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