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