New Directions in Dynamical Systems, Automatic Control and Singular Perturbations

Professor O'Reilly's book combines his engineering experience in dynamical systems, automatic control, and singular perturbations to present new results and establish new directions. It is divided into two parts, with Part 1 focusing on the fundamental conditions that small-signal physically realisable dynamical system models must satisfy, such as causality and non-singularity. Part 2 presents associated low-frequency and high-frequency system transfer-function models and examines the standard nonlinear singularly perturbed system model. This highly readable book is aimed primarily at engineers and should be read by every postgraduate.

Format: Paperback / softback
Length: 128 pages
Publication date: 28 August 2022
Publisher: Troubador Publishing

Professor O'Reilly, a renowned engineer with extensive experience in dynamical systems, automatic control, and singular perturbations, has authored a concise yet profound book that delves into these three subjects with utmost passion. In this remarkable work, Professor O'Reilly presents groundbreaking new results that have a fundamental and unifying nature, paving the way for new directions in these fields.

The book is meticulously crafted to provide a clear and engaging narrative, making it accessible to a wide audience, including engineers and postgraduate students. It is divided into two parts, Part 1 and Part 2, for the convenience of readers.

Part 1 delves into the fundamental conditions that small-signal physically realisable dynamical system models must satisfy. These conditions are causality and non-singularity, which apply to all small-signal dynamical system models, such as those encountered in electrical networks. The book reinterprets the classic works of Nyquist and Bode to establish that uncontrolled systems must also not be singular, and controlled systems must not encounter singularity. However, Part 1 goes beyond these established principles. It demonstrates that these fundamental properties, particularly non-singularity, must hold true for all small-signal system models, regardless of the number of inputs and outputs the system possesses. This groundbreaking revelation simplifies the concept of small-signal automatic control and demonstrates its seamless integration into various fields.

Part 2 focuses on singular perturbations, which are ubiquitous in dynamical systems. The book presents new associated low-frequency and high-frequency system transfer-function models with remarkable ease. These models provide a comprehensive framework for analyzing and understanding the behavior of systems subjected to singular perturbations. By applying these models, researchers and engineers can gain insights into the dynamics, stability, and control of complex systems, leading to advancements in various industries.

In conclusion, Professor O'Reilly's book is a remarkable achievement that combines engineering expertise, historical context, and a captivating narrative. It offers new insights into dynamical systems, automatic control, and singular perturbations, and establishes a solid foundation for future research and innovation. This highly readable book is a must-read for engineers, postgraduate students, and anyone interested in the field of dynamical systems.

Dimension: 234 x 156 (mm)
ISBN-13: 9781803132013