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.
Table of Contents
Introduction. Lyapunov’s Direct Method for Uncertain Systems. Stability of Uncertain Controlled Systems. Stability of Quasilinear Uncertain Systems. Stability of Large-Scale Uncertain Systems. Interval and Parametric Stability of Uncertain Systems. Stability of Solutions of Uncertain Impulsive Systems. Stability of Solutions of Uncertain Dynamic Equations on a Time Scale. Singularly Perturbed Systems with Uncertain Structure. Qualitative Analysis of Solutions of Set Differential Equations. Set Differential Equations with a Robust Causal Operator. Stability of a Set of Impulsive Equations. Comments and References.
Martynyuk, A.A.; Martynyuk-Chernienko, Yu. A.