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Stability By Liapunovs Matrix Function Method With Applications
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Book Synopsis Stability by Liapunov's Matrix Function Method with Applications by : A.A. Martynyuk
Download or read book Stability by Liapunov's Matrix Function Method with Applications written by A.A. Martynyuk and published by CRC Press. This book was released on 1998-08-03 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Book Synopsis Lyapunov Matrix Equation in System Stability and Control by : Zoran Gajic
Download or read book Lyapunov Matrix Equation in System Stability and Control written by Zoran Gajic and published by Courier Corporation. This book was released on 2008-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive treatment provides solutions to many engineering and mathematical problems related to the Lyapunov matrix equation, with self-contained chapters for easy reference. The authors offer a wide variety of techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems. 1995 edition.
Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk
Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Stability Theory at the End of the 20th Century by : A.A. Martynyuk
Download or read book Advances in Stability Theory at the End of the 20th Century written by A.A. Martynyuk and published by CRC Press. This book was released on 2002-10-03 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz by :
Download or read book Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz written by and published by Elsevier. This book was released on 2012-01-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. Best operator approximation, Non-Lagrange interpolation, Generic Karhunen-Loeve transform Generalised low-rank matrix approximation Optimal data compression Optimal nonlinear filtering
Book Synopsis Power System Stability by : M. A. Pai
Download or read book Power System Stability written by M. A. Pai and published by North-Holland. This book was released on 1981 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods of A. M. Lyapunov and Their Application by : Vladimir Ivanovich Zubov
Download or read book Methods of A. M. Lyapunov and Their Application written by Vladimir Ivanovich Zubov and published by . This book was released on 1961 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) by : Junji Kato
Download or read book Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) written by Junji Kato and published by Routledge. This book was released on 2019-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Book Synopsis Stability and Stabilization of Nonlinear Systems with Random Structures by : I. Ya Kats
Download or read book Stability and Stabilization of Nonlinear Systems with Random Structures written by I. Ya Kats and published by CRC Press. This book was released on 2002-08-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 sys
Book Synopsis Stability by Liapunov's Direct Method by : Joseph P. LaSalle
Download or read book Stability by Liapunov's Direct Method written by Joseph P. LaSalle and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory and Application of Liapunov's Direct Method by : Wolfgang Hahn
Download or read book Theory and Application of Liapunov's Direct Method written by Wolfgang Hahn and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The groundbreaking work of Russian mathematician A. M. Liapunov (1857–1918) on the stability of dynamical systems was overlooked for decades because of political turmoil. During the Cold War, when it was discovered that his method was applicable to the stability of aerospace guidance systems, interest in his research was rekindled. It has remained high ever since. This monograph on both the theory and applications of Liapunov's direct method reflects the work of a period when the theory had been studied seriously for some time and reached a degree of completeness and sophistication. It remains of interest to applied mathematicians in many areas. Topics include applications of the stability theorems to concrete problems, the converse of the main theorems, Liapunov functions with certain properties of rate of change, the sensitivity of the stability behavior to perturbations, the critical cases, and generalizations of the concept of stability.
Book Synopsis Nonlinear Dynamical Systems and Control by : Wassim M. Haddad
Download or read book Nonlinear Dynamical Systems and Control written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-09-19 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.
Book Synopsis Stability: Elements of the Theory and Application with Examples by : Anatoliy A Martynyuk
Download or read book Stability: Elements of the Theory and Application with Examples written by Anatoliy A Martynyuk and published by Sciendo. This book was released on 2020-12-20 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. The issue of constructing of the Lyapunov function is a key element in applications of the direct method, and this chapter provides several methods of constructing the function. In the end, a string of examples illustrating the use of the Lyapunov direct method is posted. Chapter five contains a detailed presentation of the comparison method and its use in the stability research. This method, being is essential part of the qualitative theory of equations, is particularly central in studies of largescale systems. In the method, some differential inequalities and Lyapunov functions allow nonlinear transformations of the original system to an equation (a system or a matrix system) of a lower dimension. The idea of delimiting and estimating so-called stability domains is developed in chapter six, where also a qualitative comparison of different stability procedures is made. The evaluation of the efficiency of various methods is conducted by applying, in each case, the same vector norm as a measure of the distance between solutions - no surprise the Lyapunov direct method wins the competition. The contrast between various method results is shown using an example of a simple second-order differential equation. Moreover, for linear systems, the notion of the best Lyapunov function is made. Manifolds of non-holonomic equations of motion are in the focus of chapter seven. Application of topological manifolds and mapping techniques prove to be effective tools in the stability research that extends more and more to advanced fields of mathematics. The chapter reviews specific applications of the Lyapunov direct method to investigations of invariant manifolds and some practical results of the topological fixed point theory. Chapter eight deals with recurrence equations, difference equations, and difference inequalities that mainly are associated with discrete dynamic systems. These types of models are usually obtained by converting the time-continuous dynamics into discrete-time dynamics by employing the Poincare-type mappings. The main objective is the stability investigation of solutions and its estimates. Chapter nine is limited to a short overview of some stability issues for delay differential equations modelling some practical processes and systems with aftereffect phenomena - the main worry is about the compensation for the loss of stability due to delay in the system. Linear models are discussed, but the emphasis is put on Lyapunov functionals for nonlinear equations. Chapter ten on partial differential equations, not including the means of discretization to the stability analysis, uses an approach based on the utilization Lyapunov functionals. The Lyapunov theory is exercised here in relation to a particular class of continuous models - it is an outline of some techniques rather than the methodology. The presented here approach is anecdotal, and it is based on specific cases and examples. Chapter eleven presents some samples of the probabilistic approach to stability matters. This category of problems is necessary when in the modelling process, it turns out that the excitations are not clear, not defined, or not repeatable. In the present considerations, the stability study is reduced to examining the stability of the trivial solution, and the focus is on the almost-sure probability. The last chapter provides a brief introduction to themes of chaos, focusing on the dependence of chaos on the Lyapunov exponent. The irregular behaviour of solutions of motion which is identified with chaos is not due to stochastic forcing or sensitive dependence on initial conditions. The real reason for it is the exponential rate of the distance between the trajectories due to nonlinearities of the system - the Lyapunov exponent is a measure of it.
Book Synopsis Stability and Control of Nonlinear Time-varying Systems by : Shuli Guo
Download or read book Stability and Control of Nonlinear Time-varying Systems written by Shuli Guo and published by Springer. This book was released on 2018-04-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents special systems derived from industrial models, including the complex saturation nonlinear functions and the delay nonlinear functions. It also presents typical methods, such as the classical Liapunov and Integral Inequalities methods. Providing constructive qualitative and stability conditions for linear systems with saturated inputs in both global and local contexts, it offers practitioners more concise model systems for modern saturation nonlinear techniques, which have the potential for future applications. This book is a valuable guide for researchers and graduate students in the fields of mathematics, control, and engineering.
Book Synopsis Applications of Liapunov Methods in Stability by : A. Halanay
Download or read book Applications of Liapunov Methods in Stability written by A. Halanay and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 1992 marks the centennial anniversary of publication of the celebrated monograph "The General Problem of Stability of Motion" written by A. M. Liapunov. This anniversary inspires to think about the way theory and applications have developed during this century. The first observation one can make is that the so-called "second method", nowadays known as the "Liapunov function method", has received more attention than the "first method"; let us also mention the study of critical cases, which brought more attention recently in connection with the study of bifurcations and with nonlinear stabilization. One of the reasons of popularity of the Liapunov function approach might be the fact that, in many situations in science and engineering, and not only in mechanics, which was the main source of inspiration for the work of Liapunov, natural Liapunov functions may be proposed, intimately connected with the properties of the processes. It is one of the purposes of this book to advocate this idea. From the mathematical viewpoint, the century after the first appear ance of Liapunov's monograph has been characterized both by general izations and by refinements of Liapunov's ideas. But we feel that the most spectacular progress is the understanding of the wide possibilities open for applications by the use of Stability Theory as constructed by Liapunov a century ago. We have tried to show some of the ideas in this direction by start ing with our personal experience in the study of some models.
Book Synopsis Stability and Stabilization of Linear Systems with Saturating Actuators by : Sophie Tarbouriech
Download or read book Stability and Stabilization of Linear Systems with Saturating Actuators written by Sophie Tarbouriech and published by Springer Science & Business Media. This book was released on 2011-08-13 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.
Book Synopsis Dynamics and Stability of Motion of Shock and Hybrid Systems by : Anatoliy A. Martynyuk
Download or read book Dynamics and Stability of Motion of Shock and Hybrid Systems written by Anatoliy A. Martynyuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-04-15 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Buy this book on degruyter.com“A href="https://www.degruyter.com/viewbooktoc/product/538686">https://www.degruyter.com/viewbooktoc/product/538686