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.

Highlights the Hamiltonian approach to singularly perturbed linear optimal control systems. Develops parallel algorithms in independent slow and fast time scales for solving various optimal linear control and filtering problems in standard and nonstandard singularly perturbed systems, continuous- and discrete-time, deterministic and stochastic, mul

This book focuses on multi-model systems, describing how to apply intelligent technologies to model complex multi-model systems by combining stochastic jumping system, neural network and fuzzy models. It focuses on robust filtering, including finite-time robust filtering, finite-frequency robust filtering and higher order moment robust filtering schemes, as well as fault detection problems for multi-model jump systems, such as observer-based robust fault detection, filtering-based robust fault detection and neural network-based robust fault detection methods. The book also demonstrates the validity and practicability of the theoretical results using simulation and practical examples, like circuit systems, robot systems and power systems. Further, it introduces readers to methods such as finite-time filtering, finite-frequency robust filtering, as well as higher order moment and neural network-based fault detection methods for multi-model jumping systems, allowing them to grasp the modeling, analysis and design of the multi-model systems presented and implement filtering and fault detection analysis for various systems, including circuit, network and mechanical systems.

Most real physical systems are nonlinear in nature. Control and?ltering of nonlinear systems are still open problems due to their complexity natures. These problem becomes more complex when the system's parameters are - certain. A common approach to designing a controller/?lter for an uncertain nonlinear system is to linearize the system about an operating point, and uses linear control theory to design a controller/?lter. This approach is successful when the operating point of the system is restricted to a certain region. H- ever, when a wide range operation of the system is required, this method may fail. ThisbookpresentsnewnovelmethodologiesfordesigningrobustH fuzzy? controllers and robustH fuzzy?lters for a class of uncertain fuzzy systems? (UFSs), uncertain fuzzy Markovian jump systems (UFMJSs), uncertain fuzzy singularly perturbed systems (UFSPSs) and uncertain fuzzy singularly p- turbed systems with Markovian jumps (UFSPS-MJs). These new meth- ologies provide a framework for designing robustH fuzzy controllers and? robustH fuzzy?lters for these classes of systems based on a Tagaki-Sugeno? (TS) fuzzy model. Solutions to the design problems are presented in terms of linear matrix inequalities (LMIs). To investigate the design problems, we?rst describe a class of uncertain nonlinear systems (UNSs), uncertain nonlinear Markovianjumpsystems(UNMJSs), uncertainnonlinearsingularlyperturbed systems(UNSPSs)anduncertainnonlinearsingularlyperturbedsystemswith Markovian jumps (UNSPS-MJs) by a TS fuzzy system with parametric - certainties and with/without Markovian jumps. Then, based on an LMI - proach, we develop a technique for designing robustH fuzzy controllers and? robustH fuzzy?lters such that a given prescribed performance index is? guaranteed.

This book proposes analysis and design techniques for Markov jump systems (MJSs) using Lyapunov function and sliding mode control techniques. It covers a range of topics including stochastic stability, finite-time boundedness, actuator-fault problem, bumpless transfer scheme, and adaptive sliding mode fault-tolerant control for uncertain MJSs. Notably, the book presents a new model for deception attacks (DAs), establishing the correlation between attacks and time delays, which should be of particular interest due to the recent increase in such attacks. The book's content is presented in a comprehensive, progressive manner, with fundamental principles introduced first before addressing more advanced techniques. The book features illustrations and tables, providing readers with a practical and intuitive approach to applying these methods in their own research. This book will prove invaluable to researchers and graduate students in control engineering and applied mathematics with an interest in the latest developments in MJSs.

The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).