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.
Introduction Parametric Stability Stability with Respect to Moving Invariant Sets Lyapunov's Direct Method for Uncertain Systems Problem Setting and Auxiliary Results Classes of Lyapunov Functions Theorems on Stability and Uniform Stability Exponential Convergence of Motions to a Moving Invariant Set Instability of Solutions with Respect to a Given Moving Set Stability with Respect to a Conditionally Invariant Moving Set Stability of Uncertain Controlled Systems Problem Setting Synthesis of Controls Convergence of Controlled Motions to a Moving Set Stabilization of Rotary Motions of a Rigid Body in an Environment with Indefinite Resistance Stability of an Uncertain Linear System with Neuron Control Conditions for Parametric Quadratic Stabilizability Stability of Quasilinear Uncertain Systems Uncertain Quasilinear System and Its Transformation Application of the Canonical Matrix-Valued Function Isolated Quasilinear Systems Quasilinear Systems with Nonautonomous Uncertainties Synchronizing of Motions in Uncertain Quasilinear Systems Stability of Large-Scale Uncertain Systems Description of a Large-Scale System Stability of Solutions with Respect to a Moving Set Application of the Hierarchical Lyapunov Function Stability of a Class of Time Invariant Uncertain Systems Interval and Parametric Stability of Uncertain Systems Conditions for the Stability of a Quasilinear System (Continued) Interval Stability of a Linear Mechanical System Parametric Stability of an Uncertain Time Invariant System Stability of Solutions of Uncertain Impulsive Systems Problem Setting Principle of Comparison with a Block-Diagonal Matrix Function Conditions for Strict Stability Application of the Vector Approach Robust Stability of Impulsive Systems Concluding Remarks Stability of Solutions of Uncertain Dynamic Equations on a Time Scale Elements of the Analysis on a Time Scale Theorems of the Direct Lyapunov Method Applications and the Discussion of the Results Singularly Perturbed Systems with Uncertain Structure Structural Uncertainties in Singularly Perturbed Systems Tests for Stability Analysis Tests for Instability Analysis Linear Systems under Structural Perturbations Qualitative Analysis of Solutions of Set Differential Equations Some Results of the General Theory of Metric Spaces Existence of Solutions of Set Differential Equations The Matrix-Valued Lyapunov Function and Its Application Stability of a Set Stationary Solution Theorems on Stability The Application of the Strengthened Lyapunov Function Boundedness Theorems Set Differential Equations with a Robust Causal Operator Preliminary Results Comparison Principle Estimates of Funnel for Solutions Test for Stability Stability of a Set of Impulsive Equations Auxiliary Results Heterogeneous Lyapunov Function Sufficient Stability Conditions Impulsive Equations with Delay under Small Perturbations Comments and References Appendix Bibliography Index