With this short book, Professor O'Reilly brings his considerable
engineering experience to bear upon three subjects close to his heart:
dynamical systems, automatic control and singular perturbations. New
results of a fundamental and unifying nature are presented in all three
areas. New directions are thereby established. Due care is taken of
historical context and motivations. This highly readable book with its
compelling physical narrative is divided into two parts, Part 1 and Part
2, for the reader's convenience. Aimed primarily at engineers, this
unusually affordable book should be read by every postgraduate.
Part 1 sets out the fundamental conditions that small-signal physically
realisable dynamical system models must satisfy. These fundamental
conditions are causality and non-singularity. They apply to all
small-signal dynamical system models, as for example arise in electrical
networks. Another important example is automatic control. Part 1 of this
book also re-interprets the classic works of Nyquist and Bode to
establish that the uncontrolled system must also not be singular; nor
must the controlled system encounter singularity. But Part 1 goes much
further. It shows that these fundamental properties, in particular
non-singularity, must obtain for all small-signal system models
regardless of how many inputs and outputs the system happens to have.
So, small-signal automatic control for instance is all of a piece. It is
that simple.
As for singular perturbations in Part 2, these little fellows simply pop
up all over the place, sometimes where you least expect them. New
associated low-frequency and high-frequency system transfer-function
models are presented with almost insolent ease. Part 2 achieves for the
frequency domain what standard singular perturbation theory does for the
time domain. Moreover, even the standard nonlinear singularly perturbed
system model does not escape scrutiny. Which model to choose? It could
be important. Part 2 is an indispensable aid to modellers across the
engineering spectrum seeking generic low-frequency and high-frequency
models for what they do.
