Uncertain Dynamical Systems：Stability and Motion Control

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.

IntroductionParametric StabilityStability with Respect to Moving Invariant SetsLyapunov’s Direct Method for Uncertain SystemsProblem Setting and Auxiliary ResultsClasses of Lyapunov FunctionsTheorems on Stability and Uniform StabilityExponential Convergence of Motions to a Moving Invariant SetInstability of Solutions with Respect to a Given Moving SetStability with Respect to a Conditionally Invariant Moving SetStability of Uncertain Controlled SystemsProblem SettingSynthesis of Controls Convergence of Controlled Motions to a Moving SetStabilization of Rotary Motions of a Rigid Body in an Environment with Indefinite ResistanceStability of an Uncertain Linear System with Neuron ControlConditions for Parametric Quadratic StabilizabilityStability of Quasilinear Uncertain SystemsUncertain Quasilinear System and Its TransformationApplication of the Canonical Matrix-Valued FunctionIsolated Quasilinear SystemsQuasilinear Systems with Nonautonomous Uncertainties Synchronizing of Motions in Uncertain Quasilinear SystemsStability of Large-Scale Uncertain SystemsDescription of a Large-Scale SystemStability of Solutions with Respect to a Moving SetApplication of the Hierarchical Lyapunov FunctionStability of a Class of Time Invariant Uncertain SystemsInterval and Parametric Stability of Uncertain SystemsConditions for the Stability of a Quasilinear System (Continued)Interval Stability of a Linear Mechanical SystemParametric Stability of an Uncertain Time Invariant SystemStability of Solutions of Uncertain Impulsive SystemsProblem SettingPrinciple of Comparison with a Block-Diagonal Matrix FunctionConditions for Strict Stability Application of the Vector ApproachRobust Stability of Impulsive SystemsConcluding RemarksStability of Solutions of Uncertain Dynamic Equations on a Time ScaleElements of the Analysis on a Time ScaleTheorems of the Direct Lyapunov Method Applications and the Discussion of the ResultsSingularly Perturbed Systems with Uncertain StructureStructural Uncertainties in Singularly Perturbed SystemsTests for Stability AnalysisTests for Instability AnalysisLinear Systems under Structural Perturbations Qualitative Analysis of Solutions of Set Differential EquationsSome Results of the General Theory of Metric SpacesExistence of Solutions of Set Differential EquationsThe Matrix-Valued Lyapunov Function and Its ApplicationStability of a Set Stationary Solution Theorems on Stability The Application of the Strengthened Lyapunov FunctionBoundedness TheoremsSet Differential Equations with a Robust Causal OperatorPreliminary ResultsComparison PrincipleEstimates of Funnel for SolutionsTest for StabilityStability of a Set of Impulsive EquationsAuxiliary ResultsHeterogeneous Lyapunov FunctionSufficient Stability ConditionsImpulsive Equations with Delay under Small PerturbationsComments and ReferencesAppendixBibliographyIndex