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Stability, Oscillations and Optimization of Systems

Stability of Motions: The Role of Multicomponent Liapunov's Functions 
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Stability, Oscillations and Optimization of Systems: Volume 1


300pp  Hbk    2007

Stability Oscillations and Optimization of Systems book series edited by A.A.Martynyuk, P.Borne and C.Cruz-Hernandez


A.A.Martynyuk, Institute of Mechanics, Kiev, Ukraine


This volume presents stability theory for ordinary differential equations, discrete systems and systems on time scale, functional differential equations and uncertain systems via multicomponent Liapunovís functions. The book sets out a new approach to solution of the problem of constructing Liapunovís functions for three classes of systems of equations. This approach is based on the application of matrix-valued function as an appropriate tool for scalar or vector Liapunov function. The volume proposes an efficient solution to the problem of robust stability of linear systems. In terms of hierarchical Liapunov function the dynamics of neural discrete-time systems is studied and includes the case of perturbed equilibrium state.


Matrix Equations, Spectral Problems and Stability of Dynamic Systems 
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Stability, Oscillations and Optimization of Systems


300pp  Hbk    2008

A.G.Mazko, Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine


This volume contains the methods for localization of eigenvalues of matrices and matrix functions, based on the construction and study of the generalized Lyapunov equation. The theory of linear equations and operators in a matrix space is developed and the known theorems on the inertia of Hermitian solutions of matrix equations are generalized. The author develops new algebraic methods for stability analysis, an evaluation of spectrum and representation of solutions of linear arbitary order differential and difference systems. The volume is intended for researchers, engineers and postgraduates interested in the theory of stability and stabilization of dynamic systems, matrix analysis and applications.


Dynamics Of Compressible Viscous Fluid 
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400pp  Hbk    2009

A. N. Guz Institute of Mechanics, Kiev, Ukraine


Dynamics of Compressible Viscous Fluid is the first monograph applied to the theory of small vibrations (motions) of rigid and elastic bodies in compressible viscous fluid. The volume also develops the methods of analysis based on the proposed general solutions of linearized Navier-Stokes equations in vector or scalar forms and considers the following problems:

  • forced harmonic vibrations and nonstationary motions of rigid bodies in moving and at rest compressible viscous fluid
  • dynamics of rigid bodies in at rest compressible fluid under the action of radiation forces from the interaction with acoustic harmonic waves
  • wave propagation in elastic bodies with initial (residual) stresses and in thin-walled elastic cylindrical shell interacting with a compressible viscous fluid.

The volume provides a useful reference text for postgraduates and researchers in applied engineering particularly wave dynamics, continuum mechanics and fluid mechanics.


Advances In Chaotic Dynamics and Applications 
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280pp  Hbk    2010

A. A. Martynyuk and C. Cruz- Hernandez


This multiauthor volume provides a useful and timely reference for postgraduates and researchers in applied mathematics, mechanics and engineering.


Contents include:

On three definitions of chaos

B. Aulbach and B. Kieninger


Hausdorff dimension estimates by use of a tubular Caratheodory structure and their application to stability theory.


G. A. Leonov, K. Gelfert and V. Reitmann


Chaotic control systems


T. L. Vincent


The relationship between pullback, forward and global attractors on nonautonomous dynamical systems.


D. N. Cheban, P. E. Kloeden and B. Schmalfuss


Control of chaos in a convective loop system.


A. K. M. Murshed, B. Huang and K. Nandakumar


Synchronization of time-delay Chua's oscillator with application to secure communication.


C. Cruz-Hernandez


Topological sequence entropy and chaos of star maps.


J. S. Canovas


Output synchronization of chaotic systems: model-matching approach with application to secure communication.


D. Lopez-Mancilla and C. Cruz-Hernandez


Stabilization of Linear Systems 
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430pp  Hbk    2011

G.A. Leonov, St Petersburg University


The volume presents a full survey of stabilization theory for linear control systems which is a research area of increasing importance.  New methods of low-frequency and high-frequence stabilization are introduced and many significant results are included.  Poincare mapping is constructed, realizing the embedding of unstable manifold.  Contents include:


Transfer function and frequency response;

Controllability amd observation;

Stationary stabilization of linear systems;

Stabilization of discrete systems.


This volume is intended for researchers, engineers and postgraduates interested in the dynamic systems, applied differential equations and control theory.


Lyapunov Exponents And Stability 
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2012 380pp Hbk

N. A. Izobov. Institute of Mathematics

National Academy of Sciences of Belarus, Minsk


The monograph contains the necessary information from the modern theory

of Lyapunov characteristic exponents of ordinary linear differential systems.

It is mainly dedicated to the brief description of the results obtained by the

author, connected with the development of the following parts: the theory

of Perron lower exponents, the freezing method, the theory of exponential

and sigma-exponents and their connection with characteristic, central,

and general exponents, the dependence of characteristic exponents of linear

systems on exponentially decreasing perturbation and the theory of their

stability with respect to small perturbations. As an application of those

results the author considered the Lyapunov problem on the exponential

stability of an ordinary differential system by linear approximation. In the

monograph the method of rotations by V.M.Millionschikov is systematically

used. This volume is intended for specialists in the asymptotic theory of

ordinary differential systems and the stability theory, for post-graduates

and students specialized in the field of differential equations.



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