Martynyuk / Martynyuk-Chernienko Uncertain Dynamical Systems

Stability and Motion Control
1. Auflage 2011
ISBN: 978-1-4398-7687-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 310 Seiten

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

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.

Zielgruppe

Pure and applied mathematicians, applied physicists, industrial engineers, operations researchers, and upper-level undergraduate and graduate students in mathematics and engineering.

Autoren/Hrsg.

Martynyuk, A.A.

Martynyuk-Chernienko, Yu. A.

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

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