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This volume in the newly established series Advances in Delays and
Dynamics (ADD@S) provides a collection of recent results on the
design and analysis of Low Complexity Controllers for Time Delay
Systems. A widely used indirect method to obtain low order
controllers for time delay systems is to design a controller for
the reduced order model of the plant. In the dual indirect
approach, an infinite dimensional controller is designed first for
the original plant model; then, the controller is approximated by
keeping track of the degradation in performance and stability
robustness measures. The present volume includes new techniques
used at different stages of the indirect approach. It also includes
new direct design methods for fixed structure and low order
controllers. On the other hand, what is meant by low complexity
controller is not necessarily low order controller. For example,
Smith predictor or similar type of controllers include a copy of
the plant internally in the controller, so they are technically
infinite dimensional. However, they have very nice numerical
properties from the point of reliable implementation. Therefore,
such predictor-based controllers are considered as low complexity.
This book includes new predictor-based design techniques, with
several application examples.
Since its inception in the early 1980s, H( optimization theory has
become the control methodology of choice in robust feedback
analysis and design. The purpose of this monograph is to present,
in a tutorial fashion, a self contained operator theoretic approach
to the H( control for disturbed parameter systems, that is, systems
which admit infinite dimensional state spaces. Such systems arise
for problems modelled by partial differential equations or which
have time delays. Besides elucidating the mathematics of H(
control, extensive treatment is given to its physical and
engineering underpinnings. The techniques given in the book are
carefully illustrated by two benchmark problems: an unstable system
with a time delay which comes from the control of the X-29, and the
control of a Euler-Bernoulli flexible beam with Kelvin-Voigt
damping.
This book presents new computational tools for the H control of
distributed parameter systems in which transfer functions are
considered as input-output descriptions for the plants to be
controlled. The emphasis is on the computation of the controller
parameters and reliable implementation. The authors present recent
studies showing that the simplified skew Toeplitz method is
applicable to a wide class of systems, supply detailed examples
from systems with time delays and various engineering applications,
and discuss reliable implementation of the controller, complemented
by a software based on MATLAB (R). Frequency Domain Techniques for
H Control of Distributed Parameter Systems is intended for advanced
undergraduate and early graduate students interested in robust
control of distributed parameter systems-time delay systems-as well
as researchers and engineers working in related fields. It can be
used in the following courses: Introduction to Robust Control with
Applications to Distributed Parameter Systems and Introduction to
Robust Control with Applications to Time Delay Systems.
This brief examines a deterministic, ODE-based model for gene
regulatory networks (GRN) that incorporates nonlinearities and
time-delayed feedback. An introductory chapter provides some
insights into molecular biology and GRNs. The mathematical tools
necessary for studying the GRN model are then reviewed, in
particular Hill functions and Schwarzian derivatives. One chapter
is devoted to the analysis of GRNs under negative feedback with
time delays and a special case of a homogenous GRN is considered.
Asymptotic stability analysis of GRNs under positive feedback is
then considered in a separate chapter, in which conditions leading
to bi-stability are derived. Graduate and advanced undergraduate
students and researchers in control engineering, applied
mathematics, systems biology and synthetic biology will find this
brief to be a clear and concise introduction to the modeling and
analysis of GRNs.
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