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

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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

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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

A novel, very simple chaotic oscillator is described. It is intended for training laboratories accompanying courses on nonlinear dynamics and chaos for undergraduate, postgraduate and PhD students. The oscillator consists of an operational amplifier, an LCR resonance loop, an extra capacitor, a diode as a nonlinear element and three auxiliary resistors. Chaotic oscillations are demonstrated both experimentally and numerically.

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A simple chaotic oscillator for educational purposes

Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems

We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free unstable periodic orbits in nonautonomous chaotic systems. To improve the global control performance we introduce a two-step control algorithm. The problem of a linear stability of the system under delayed feedback control is treated analytically. Theoretical results are confirmed by electronic circuit experiments for a forced double-well oscillator.

Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: theory and experiment.

Secure communication via chaotic synchronization is demonstrated using dynamical systems governed by delay deferential equations. Strange attractors of such systems can have an arbitrarily large number of positive Lyapunov exponents giving rise to very complex time signals. This features can provide high security of masked messages.

Transmission of Signals via Synchronization of Chaotic Time-Delay Systems

We propose an algorithm of coupling design for a long-term anticipating synchronization of chaos and demonstrate its efficacy for typical chaotic systems: namely, the Rossler system, the double-scroll Chua circuit, and the Lorenz system. The maximum prediction time attained with our algorithm is several times larger than with the diagonal coupling usually used in the literature.

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Kestutis Pyragas

Papers

A simple chaotic oscillator for educational purposes

Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems

Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: theory and experiment.

Transmission of Signals via Synchronization of Chaotic Time-Delay Systems

Coupling design for a long-term anticipating synchronization of chaos.