Stability Analysis

Danksagung
Kurzfassung
Abstract
Contents
List of Figures
List of Tables
1 Introduction
	1.1 Motivation
	1.2 Main Goals
2 Dynamic Local Model Networks
	2.1 Introduction
	2.2 Architecture of Dynamic LocalModel Networks
	2.3 Review of the Hierarchical Discriminant Tree, Hametner:2007,Hametner:2012cv
3 Open Loop Stability Analysis
	3.1 Introduction
	3.2 Concepts of Stability, [4]
	3.3 Open Loop Stability Analysis using Eigenvalue Analysis
	3.4 Open Loop Stability Analysis using Lyapunov's Direct Method
		3.4.1 A Simple Motivating Example
		3.4.2 General
		3.4.3 Lyapunov's Direct Method
		3.4.4 State-Space Notation for Open Loop Stability Analysis
		3.4.5 Common Quadratic Lyapunov Approach for Discrete-Time Local Model Networks
		3.4.6 Piecewise Quadratic Lyapunov Approach for Discrete-Time Local Model Networks
		3.4.7 Determination of the Convex Hull of Local Model Networks with a Hierarchical Discriminant Tree
		3.4.8 Determination of the Upper Bounds of the Uncertainty Terms
		3.4.9 Example
		3.4.10 Fuzzy Lyapunov Approach for Discrete-Time Local Model Networks
	3.5 Transition Determination
		3.5.1 General
		3.5.2 Methodology
		3.5.3 Examples
	3.6 Example: Comparison of the Treated Lyapunov Approaches
4 Closed-Loop Stability Analysis and Controller Design
	4.1 Introduction
	4.2 State-Feedback Control Law
	4.3 Local Model Network in State-Space Notation for Closed-Loop Stability Analysis and Controller Design
	4.4 Closed-Loop Stability Analysis using the Common Quadratic Lyapunov Approach
	4.5 Closed-Loop Stability Analysis using the Fuzzy Lyapunov Approach
	4.6 State-Space Controller Design using the Common Quadratic Lyapunov Approach
	4.7 State-Space Controller Design using the Fuzzy Lyapunov Approach
	4.8 Optimal Input Gain and Offset Compensator Design
5 PID Controller Design
	5.1 Introduction
		5.1.1 Discrete-time PID Control Algorithm
		5.1.2 PID Control Algorithm for Local Model Networks
	5.2 Closed-Loop in State-Space Notation
		5.2.1 Basic Concept
		5.2.2 Construction of the System Matrices
		5.2.3 Feedback Loop
	5.3 Stability Criterion
	5.4 Controller Design
		5.4.1 iLMI Procedure
		5.4.2 Multi-Objective GA
6 Conclusion and Outlook
A LMI Solver Comparison
	Introduction
	Comparison
References