Nonlinear Time-Delay Systems: A Geometric Approach

✍ Scribed by Claudia Califano; Claude H. Moog

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 113
• Series: SpringerBriefs in Electrical and Computer Engineering: Control, Automation and Robotics
• Category: Library

✦ Synopsis

This brief focuses on the structural properties of nonlinear time-delay systems. It provides a link between coverage of fundamental theoretical properties and advanced control algorithms, as well as suggesting a path for the generalization of the differential geometric approach to time-delay systems .

The brief begins with an introduction to a class of single-input nonlinear time-delay systems. It then focuses on geometric methods treating them and offers a geometric framework for integrability. The book has chapters dedicated to the accessibility and observability of nonlinear time-delay systems, allowing readers to understand the systems in a well-ordered, structured way. Finally, the brief concludes with applications of integrability and the control of single-input time-delay systems.

This brief employs exercises and examples to familiarize readers with the time-delay context. It is of interest to researchers, engineers and postgraduate students who work in the area of nonlinear control systems.

✦ Table of Contents

Preface
Contents
1 Preliminaries
1.1 The Class of Systems
1.2 Integrability
1.3 Geometric Behavior
1.4 Accessibility and Observability Properties
1.5 Notation
1.6 Recalls on Non-commutative Algebra
2 Geometric Tools for Time-Delay Systems
2.1 The Initialization of the Time-Delay System Versus the Initialization of the Delay-Free Extended System
2.2 Non-independence of the Inputs of the Extended System
2.3 The Differential Form Representation
2.4 Generalized Lie Derivative and Generalized Lie Bracket
2.5 Some Remarks on the Polynomial Lie Bracket
2.6 The Action of Changes of Coordinates
2.7 The Action of Static State Feedback Laws
2.8 Problems
3 The Geometric Framework—Results on Integrability
3.1 Some Remarks on Left and Right Integrability
3.2 Integrability of a Right-Submodule
3.2.1 Involutivity of a Right-Submodule Versus its Integrability
3.2.2 Smallest 0-Integrable Right-Submodule Containing Δ(δ]
3.2.3 p-Integrability
3.2.4 Bicausal Change of Coordinates
3.3 Integrability of a Left-Submodule
3.4 Problems
4 Accessibility of Nonlinear Time-Delay Systems
4.1 The Accessibility Submodules in the Delay Context
4.2 A Canonical Decomposition with Respect to Accessibility
4.3 On the Computation of the Accessibility Submodules
4.4 On t-Accessibility of Time-Delay Systems
4.5 Problems
5 Observability
5.1 Decomposing with Respect to Observability
5.1.1 The Case of Autonomous Systems
5.2 On Regular Observability for Time-Delay Systems
5.3 Problems
6 Applications of Integrability
6.1 Characterization of the Chained Form with Delays
6.2 Input–Output Feedback Linearization
6.2.1 Introductory Examples
6.2.2 Static Output Feedback Solutions
6.2.3 Hybrid Output Feedback Solutions
6.3 Input-State Linearization
6.3.1 Introductory Example
6.3.2 Solution
6.4 Normal Form
6.5 Problems
Series Editor Biographies
References