An introductory chapter highlights basics concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples and LMI synthesis methods and design approaches.

An introductory chapter highlights basics concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples and LMI synthesis methods and design approaches.

Saturated Switching Systems treats the problem of actuator saturation, inherent in all dynamical systems by using two approaches: positive invariance in which the controller is designed to work within a region of non-saturating linear behaviour; and saturation technique which allows saturation but guarantees asymptotic stability. The results obtained are extended from the linear systems in which they were first developed to switching systems with uncertainties, 2D switching systems, switching systems with Markovian jumping and switching systems of the Takagi-Sugeno type. The text represents a thoroughly referenced distillation of results obtained in this field during the last decade. The selected tool for analysis and design of stabilizing controllers is based on multiple Lyapunov functions and linear matrix inequalities. All the results are illustrated with numerical examples and figures many of them being modelled using MATLAB®. Saturated Switching Systems will be of interest to academic researchers in control systems and to professionals working in any of the many fields where systems are affected by saturation including: chemical and pharmaceutical batch processing, manufacturing (for example in steel rolling), air-traffic control, and the automotive and aerospace industries.

In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.

This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.

This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models.The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.