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This monograph presents a collection of results, observations, and
examples related to dynamical systems described by linear and
nonlinear ordinary differential and difference equations. In
particular, dynamical systems that are susceptible to analysis by
the Liapunov approach are considered. The naive observation that
certain "diagonal-type" Liapunov functions are ubiquitous in the
literature attracted the attention of the authors and led to some
natural questions. Why does this happen so often? What are the spe
cial virtues of these functions in this context? Do they occur so
frequently merely because they belong to the simplest class of
Liapunov functions and are thus more convenient, or are there any
more specific reasons? This monograph constitutes the authors'
synthesis of the work on this subject that has been jointly
developed by them, among others, producing and compiling results,
properties, and examples for many years, aiming to answer these
questions and also to formalize some of the folklore or "cul ture"
that has grown around diagonal stability and diagonal-type Liapunov
functions. A natural answer to these questions would be that the
use of diagonal type Liapunov functions is frequent because of
their simplicity within the class of all possible Liapunov
functions. This monograph shows that, although this obvious
interpretation is often adequate, there are many in stances in
which the Liapunov approach is best taken advantage of using
diagonal-type Liapunov functions. In fact, they yield necessary and
suffi cient stability conditions for some classes of nonlinear
dynamical systems."
This monograph presents a collection of results, observations, and
examples related to dynamical systems described by linear and
nonlinear ordinary differential and difference equations. In
particular, dynamical systems that are susceptible to analysis by
the Liapunov approach are considered. The naive observation that
certain "diagonal-type" Liapunov functions are ubiquitous in the
literature attracted the attention of the authors and led to some
natural questions. Why does this happen so often? What are the spe
cial virtues of these functions in this context? Do they occur so
frequently merely because they belong to the simplest class of
Liapunov functions and are thus more convenient, or are there any
more specific reasons? This monograph constitutes the authors'
synthesis of the work on this subject that has been jointly
developed by them, among others, producing and compiling results,
properties, and examples for many years, aiming to answer these
questions and also to formalize some of the folklore or "cul ture"
that has grown around diagonal stability and diagonal-type Liapunov
functions. A natural answer to these questions would be that the
use of diagonal type Liapunov functions is frequent because of
their simplicity within the class of all possible Liapunov
functions. This monograph shows that, although this obvious
interpretation is often adequate, there are many in stances in
which the Liapunov approach is best taken advantage of using
diagonal-type Liapunov functions. In fact, they yield necessary and
suffi cient stability conditions for some classes of nonlinear
dynamical systems."
This book introduces optimal control methods, formulated as
optimization problems, applied to business dynamics problems.
Business dynamics refers to a combination of business management
and financial objectives embedded in a dynamical system model. The
model is subject to a control that optimizes a performance index
and takes both management and financial aspects into account.
Business Dynamics Models: Optimization-Based One Step Ahead Optimal
Control includes solutions that provide a rationale for the use of
optimal control and guidelines for further investigation into more
complex models, as well as formulations that can also be used in a
so-called flight simulator mode to investigate different complex
scenarios. The text offers a modern programming environment
(Jupyter notebooks in JuMP/Julia) for modeling, simulation, and
optimization, and Julia code and notebooks are provided on a
website for readers to experiment with their own examples. This
book is intended for students majoring in applied mathematics,
business, and engineering. The authors use a
formulation-algorithm-example approach, rather than the classical
definition-theorem-proof, making the material understandable to
senior undergraduates and beginning graduates.
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