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This self-contained book provides systematic instructive analysis
of uncertain systems of the following types: ordinary differential
equations, impulsive equations, equations on time scales,
singularly perturbed differential equations, and set differential
equations. Each chapter contains new conditions of stability of
unperturbed motion of the above-mentioned type of equations, along
with some applications. Without assuming specific knowledge of
uncertain dynamical systems, the book includes many fundamental
facts about dynamical behaviour of its solutions. Giving a concise
review of current research developments, Uncertain Dynamical
Systems: Stability and Motion Control Details all proofs of
stability conditions for five classes of uncertain systems Clearly
defines all used notions of stability and control theory Contains
an extensive bibliography, facilitating quick access to specific
subject areas in each chapter Requiring only a fundamental
knowledge of general theory of differential equations and calculus,
this book serves as an excellent text for pure and applied
mathematicians, applied physicists, industrial engineers,
operations researchers, and upper-level undergraduate and graduate
students studying ordinary differential equations, impulse
equations, dynamic equations on time scales, and set differential
equations.
This self-contained book provides systematic instructive analysis
of uncertain systems of the following types: ordinary differential
equations, impulsive equations, equations on time scales,
singularly perturbed differential equations, and set differential
equations. Each chapter contains new conditions of stability of
unperturbed motion of the above-mentioned type of equations, along
with some applications. Without assuming specific knowledge of
uncertain dynamical systems, the book includes many fundamental
facts about dynamical behaviour of its solutions. Giving a concise
review of current research developments, Uncertain Dynamical
Systems: Stability and Motion Control Details all proofs of
stability conditions for five classes of uncertain systems Clearly
defines all used notions of stability and control theory Contains
an extensive bibliography, facilitating quick access to specific
subject areas in each chapter Requiring only a fundamental
knowledge of general theory of differential equations and calculus,
this book serves as an excellent text for pure and applied
mathematicians, applied physicists, industrial engineers,
operations researchers, and upper-level undergraduate and graduate
students studying ordinary differential equations, impulse
equations, dynamic equations on time scales, and set differential
equations.
"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."
"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."
From the Preface: This book constitutes an up to date presentation
and development of stability theory in the Liapunov sense with
various extensions and applications. Precise definitions of well
known and new stability properties are given by the authors who
present general results on the Liapunov stability properties of
non-stationary systems which are out of the classical stability
theory framework. The study involves the use of time varying sets
and is broadened to time varying Lur'e-Postnikov systems and
singularly perturbed systems... According to the amount and
importance of definitions and stability criteria presented I
consider that this book, initially published in Russian, represents
the most complete one on stability theory proposed at this date. It
interests all people concerned with stability problems in the
largest sense and with security, reliability and robustness.
"Professor Pierre Borne, Lille, France" #1
Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of theory stability and theory of stabilization of nonlinear systems with random structure in terms of new development of the direct Lyapunov's method. The analysis is focused on dynamic systems with random Markov parameters. This high-level monograph would be of great interest to 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. eBook available with sample pages: 0203218892
Asymptotic Methods in Resonance Analytical Dynamics presents new
asymptotic methods for the analysis and construction of solutions
(mainly periodic and quasiperiodic) of differential equations with
small parameters. Along with some background material and theory
behind these methods, the authors also consider a variety of
problems and applications in nonlinear mechanics and oscillation
theory. The methods examined are based on two types: the
generalized averaging technique of Krylov-Bogolubov and the
numeric-analytical iterations of Lyapunov-PoincarA(c). This text
provides a useful source of reference for postgraduates and
researchers working in this area of applied mathematics.
This volume presents surveys and research papers on aspects of the modern theory of stability and some applications. The volume consists of four sections presenting the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of direct method; stability of solutions to periodic differential systems; and selected applications. This book will be of great interest to postgraduates and researchers in the fields of maths and engineering. eBook available with sample pages: 0203166574
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