**Author** - A.A. Martynyuk

**Publisher** - CRC Press

**Pages** - 368

**ISBN** - 9780203166574

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## Advances In Stability Theory At The End Of The 20th Century

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### Advances in Stability Theory at the End of the 20th Century :

*Mathematics*Download Read Now

**Detail** - This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics.

### Stability Theory for Dynamic Equations on Time Scales :

*Mathematics* **Author** - Anatoly A. Martynyuk

**Publisher** - Birkhäuser

**Pages** - 223

**ISBN** - 3319422138

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**Detail** - This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

### Functional Differential Equations : Advances and Applications

*Mathematics* **Author** - Constantin Corduneanu, Yizeng Li, Mehran Mahdavi

**Publisher** - John Wiley & Sons

**Pages** - 368

**ISBN** - 1119189470

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**Detail** - Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

### Stability and Stabilization of Nonlinear Systems with Random Structures :

*Mathematics* **Author** - I. Ya Kats, A.A. Martynyuk

**Publisher** - CRC Press

**Pages** - 256

**ISBN** - 9780203218891

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**Detail** - Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic systems with random Markov parameters. This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.

### Lyapunov Functions in Differential Games :

*Mathematics* **Author** - Vladislav I Zhukovskiy

**Publisher** - CRC Press

**Pages** - 304

**ISBN** - 9780415273411

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**Detail** - A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.

### Stability by Liapunov's Matrix Function Method with Applications :

*Mathematics* **Author** - A.A. Martynyuk

**Publisher** - CRC Press

**Pages** - 296

**ISBN** - 9780824701918

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**Detail** - "Provides a systematic study of matrix Liapunov functions, incorporating new techniques for the qualitative analysis of nonlinear systems encountered in a wide variety of real-world situations."

### Mathematical Reviews :

*Mathematics* **Author** -

**Publisher** -

**Pages** -

**ISBN** -

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### Qualitative Methods in Nonlinear Dynamics : Novel Approaches to Liapunov's Matrix Functions

*Mathematics* **Author** - A.A. Martynyuk

**Publisher** - CRC Press

**Pages** - 320

**ISBN** - 9780824707354

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**Detail** - "Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."

### Stability of Motion : The Role of Multicomponent Liapunov's Functions

*Lyapunov functions* **Author** - Anatoliĭ Andreevich Martyni͡uk

**Publisher** -

**Pages** - 322

**ISBN** - 9781904868453

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**Detail** - This volume presents stability theory for ordinary differential equations, discrete systems and systems on time scale, functional differential equations and uncertain systems via multicomponent Liapunov's functions. The book sets out a new approach to solution of the problem of constructing Liapunov's 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.

### American Book Publishing Record :

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### DCDS-A :

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### End of History and the Last Man :

*History* **Author** - Francis Fukuyama

**Publisher** - Simon and Schuster

**Pages** - 464

**ISBN** - 1416531785

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**Detail** - Ever since its first publication in 1992, The End of History and the Last Man has provoked controversy and debate. Francis Fukuyama's prescient analysis of religious fundamentalism, politics, scientific progress, ethical codes, and war is as essential for a world fighting fundamentalist terrorists as it was for the end of the Cold War. Now updated with a new afterword, The End of History and the Last Man is a modern classic.

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