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This monograph is an up-to-date presentation of the analysis and
design of singular Markovian jump systems (SMJSs) in which the
transition rate matrix of the underlying systems is generally
uncertain, partially unknown and designed. The problems addressed
include stability, stabilization, H∞ control and filtering,
observer design, and adaptive control. applications of Markov
process are investigated by using Lyapunov theory, linear matrix
inequalities (LMIs), S-procedure and the stochastic Barbalat’s
Lemma, among other techniques. Features of the book include:
·        study of
the stability problem for SMJSs with general transition rate
matrices (TRMs);
·       Â
stabilization for SMJSs by TRM design, noise control,
proportional-derivative and partially mode-dependent control, in
terms of LMIs with and without equation constraints;
·       Â
mode-dependent and mode-independent H∞ control solutions with
development of a type of disordered controller;
·       Â
observer-based controllers of SMJSs in which both the designed
observer and controller are either mode-dependent or
mode-independent;
·       Â
consideration of robust H∞ filtering in terms of uncertain TRM or
filter parameters leading to a method for totally mode-independent
filtering
·       Â
development of LMI-based conditions for a class of adaptive state
feedback controllers with almost-certainly-bounded estimated error
and almost-certainly-asymptotically-stable corres ponding
closed-loop system states
·       Â
applications of Markov process on singular systems with norm
bounded uncertainties and time-varying delays Analysis and Design
of Singular Markovian Jump Systems contains valuable reference
material for academic researchers wishing to explore the area. The
contents are also suitable for a one-semester graduate course.
This monograph is an up-to-date presentation of the analysis and
design of singular Markovian jump systems (SMJSs) in which the
transition rate matrix of the underlying systems is generally
uncertain, partially unknown and designed. The problems addressed
include stability, stabilization, H control and filtering, observer
design, and adaptive control. applications of Markov process are
investigated by using Lyapunov theory, linear matrix inequalities
(LMIs), S-procedure and the stochastic Barbalat's Lemma, among
other techniques. Features of the book include: * study of the
stability problem for SMJSs with general transition rate matrices
(TRMs); * stabilization for SMJSs by TRM design, noise control,
proportional-derivative and partially mode-dependent control, in
terms of LMIs with and without equation constraints; *
mode-dependent and mode-independent H control solutions with
development of a type of disordered controller; * observer-based
controllers of SMJSs in which both the designed observer and
controller are either mode-dependent or mode-independent; *
consideration of robust H filtering in terms of uncertain TRM or
filter parameters leading to a method for totally mode-independent
filtering * development of LMI-based conditions for a class of
adaptive state feedback controllers with almost-certainly-bounded
estimated error and almost-certainly-asymptotically-stable corres
ponding closed-loop system states * applications of Markov process
on singular systems with norm bounded uncertainties and
time-varying delays Analysis and Design of Singular Markovian Jump
Systems contains valuable reference material for academic
researchers wishing to explore the area. The contents are also
suitable for a one-semester graduate course.
This book is intended as a one-semester course in general topology,
a.k.a. point-set topology, for undergraduate students as well as
first-year graduate students. Such a course is considered a
prerequisite for further studying analysis, geometry, manifolds,
and certainly, for a career of mathematical research. Researchers
may find it helpful especially from the comprehensive
indices.General topology resembles a language in modern
mathematics. Because of this, the book is with a concentration on
basic concepts in general topology, and the presentation is of a
brief style, both concise and precise. Though it is hard to
determine exactly which concepts therein are basic and which are
not, the author makes efforts in the selection according to
personal experience on the occurrence frequency of notions in
advanced mathematics, and to related books that have received
admirable reviews.This book also contains exercises for each
chapter with selected solutions. Interrelationships among concepts
are taken into account frequently. Twelve particular topological
spaces are repeatedly exploited, which serve as examples to learn
new concepts based on old ones.
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