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Full Description
This book offers a systematic platform for the theory of Boolean matrix and its application in logical dynamical systems. As a special kind of non-negative matrix, Boolean matrix has wide applications in graph theory, discrete-event system, game theory, clustering analysis, and so on. Due to the special operations between Boolean matrices, there exist some special mathematical properties for Boolean polynomial and Boolean vector space, which necessitate a general theory of Boolean matrix. Furthermore, logical dynamical systems have received recent attention from systems biology, information security, artificial intelligence, etc. The development of logical dynamical systems needs the mathematical foundation of Boolean matrix and logical matrix. Therefore, it is necessary to explore the relation between Boolean matrix theory and logical dynamical systems.
To our best knowledge, there are no published books available on both Boolean matrix theory and logical dynamical systems. This book aims to provide some recent insightful results to meet this gap. It can serve as a textbook for scholars and students of mathematics, cybernetics, biology and artificial intelligence. Especially, the book is an important reference for readers who are interested in Boolean matrix theory and logical dynamical systems.
Contents
Preliminaries matrix multiplications matrix expression of logic boolean matrix.- Boolean polynomial.- Boolean determinant and equations.- Boolean vector space.- Generalized inverse of boolean matrix.- Characteristic vector of boolean matrix.- Analysis of logical networks stability controllability and observability of logical networks.- Control design of logical control networks reachable set approach sample data control event triggered control control lyapunov function robust control.- Generalized logical networks delayed logical network impulsive logical network asynchronous logical network applications of logical networks.- Switched logical networks.- Probabilistic logical networks.- Large scale logical networks.
