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

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

From the Publisher:
A comprehensive treatment of model-based fuzzy control systems
This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications.
Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model.
This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field.
Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

Controlling chaos

Recurrence plots for the analysis of complex systems

We analyze the influence of high-frequency current stimulation on spontaneous neuronal activity and show that it may cause a death of spontaneous low-frequency oscillations. We demonstrate the universality of this effect for typical neuron models such as FitzHugh–Nagumo, Morris–Lecar, and Hodgkin–Huxley neurons as well as for the  normal form of the  supercritical Hopf bifurcation. Using a multiple scale method we separate the solutions of the neuron equations into slow and fast components and derive averaged equations for the slow components. The mechanism of suppression of neuronal activity is explained by an analysis of the bifurcations in the averaged equations governing the dynamics of the slow motion. Our results may contribute to the understanding of therapeutic effects of high-frequency deep brain stimulation, the golden standard for the treatment of medically refractory patients suffering from Parkinson’s disease. Furthermore, our study enables hypotheses concerning possible improvements of high-frequency deep brain stimulation.

/pdf/suppression-of-spontaneous-oscillations-in-high-frequency-5e5kfv3nhu.pdf

Suppression of spontaneous oscillations in high-frequency stimulated neuron models

The problem of controlling synchrony in bistable networks, which possess coherent and incoherent attractors in a certain range of parameters, is considered. Along with the known Kuramoto-type models, we introduce the bistable networks consisting of all-to-all coupled noisy FitzHugh-Nagumo neurons as well as chaotic Rulkov neurons. We suggest two different algorithms to switch the bistable networks from the stable coherent state to the stable incoherent state. One of them is an act-and-wait control method, which utilizes the mean field measurements and homogeneous time delayed feedback perturbations with the periodically switched on and off feedback gain. We show that this algorithm is efficient for the globally coupled populations. Another algorithm is based on the multisite coordinated reset stimulation. The algorithm is nonfeedback, but it uses inhomogeneous perturbations and is efficient even for the networks with a complex scale-free topology. In addition to the numerical analysis of finite-size networks, the analytical results for the Kuramoto-type models in the thermodynamic limit are presented.

Eliminating synchronization in bistable networks

It is demonstrated theoretically that a stable and tunable semiconductor oscillator can be designed by using a novel method of chaos control. By application of a small time-continuous delayed feedback voltage control signal, different unstable periodic orbits embedded in the chaotic attractor of a semiconductor can be stabilized. Thus different modes of self-generated periodic voltage oscillations can be selected, for example by choosing an appropriate delay time. This is illustrated for two different oscillation mechanisms involving hot-carrier transport: (i) self-generated oscillations under crossed electric and magnetic fields in the regime of low-temperature impurity breakdown (dynamic Hall effect), and (ii) driven real-space transfer oscillations in modulation-doped heterostructures.

Tuning of semiconductor oscillators by chaos control

The Schottky-barrier diodes are commonly classified as low-noise high-speed semiconductor devices for high frequency and microwave applications When reverse-biased at the breakdown voltages they can be employed as noise sources characterized by an effective noise temperature from 10 K to 10 K [1] In the present paper we describe high-power noise generator with a Schottky diode Actually it is a dynamical noise (chaos) generator similar to the tunnel diode oscillator driven by external sinusoidal voltage [2, 3] The main shortcoming of the externally driven (non-autonomous) systems is that sharp peaks do appear in the power spectra at the drive frequency and its higher harmonics In contrast, the dynamical noise generator suggested in this paper is an autonomous one, providing essentially smoother power spectra Two experimental prototypes of the oscillator operating at different fundamental frequencies f∗ = 1/2π √ LC have been investigated The first one has been set at low megahertz frequency (f∗ ≈ 1 MHz), meanwhile the second one has been tuned to operate at high megahertz frequency (f∗ ≈ 100 MHz)

/pdf/application-of-ultrafast-schottky-diodes-to-high-megahertz-3kpqls8zjo.pdf

Kestutis Pyragas

Papers

Suppression of spontaneous oscillations in high-frequency stimulated neuron models

Eliminating synchronization in bistable networks

Tuning of semiconductor oscillators by chaos control

Application of Ultrafast Schottky Diodes to High Megahertz Chaotic Oscillators

Anticipatory synchronization via low-dimensional filters