Leonov Gennady A's Books

Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

By: Gennady A Leonov,Dimitrij V Ponomarenko,V B Smirnova

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Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

By: Gennady A Leonov,Dimitrij V Ponomarenko,V B Smirnova

This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.

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Page Count

512

Publisher

World Scientific

Published Date

ISBN 10

9814500909

ISBN 13

9789814500906

Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities

By: Gennady A Leonov,Vladimir A Yakubovich,Arkadii Kh Gelig

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Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities

By: Gennady A Leonov,Vladimir A Yakubovich,Arkadii Kh Gelig

This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.

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Page Count

351

Publisher

World Scientific

Published Date

ISBN 10

9814483486

ISBN 13

9789814483483

Mathematical Problems Of Control Theory: An Introduction

By: Gennady A Leonov

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Mathematical Problems Of Control Theory: An Introduction

By: Gennady A Leonov

This book shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. In many cases, by using this apparatus, far-reaching generalizations have been made, and its further development will have an important effect on many fields of mathematics.In the book a way is demonstrated in which the study of the Watt flyball governor has given rise to the theory of stability of motion. The criteria of controllability, observability, and stabilization are stated. Analysis is made of dynamical systems, which describe an autopilot, spacecraft orientation system, controllers of a synchronous electric machine, and phase-locked loops. The Aizerman and Brockett problems are discussed and an introduction to the theory of discrete control systems is given.

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Page Count

182

Publisher

World Scientific

Published Date

ISBN 10

981449058X

ISBN 13

9789814490580

Book's by Leonov Gennady A

Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities

Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities

Mathematical Problems Of Control Theory: An Introduction

Mathematical Problems Of Control Theory: An Introduction

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