Guoliang Wang

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.

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, H8 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 H8 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 H8 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 corresponding closed-loop system states· applications of Markov process on singular systems with norm bounded uncertainties and time-varying delaysAnalysis 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, H8 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 H8 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 H8 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 corresponding closed-loop system states· applications of Markov process on singular systems with norm bounded uncertainties and time-varying delaysAnalysis 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.