From Boolean Matrix Theory to Logical Dynamical Systems

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.

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.

Haitao Li, is currently a professor at the School of Mathematics and Statistics, Shandong Normal University. From Jan. 2014 to Jan. 2015, he worked as a Research Fellow in Nanyang Technological University, Singapore. His research interests include finite-value systems, networked control systems, game-theoretic control, etc. He received the Young Experts of Taishan Scholar Project in 2019, the Second Class Prize of The Natural Science Award of Shandong Province in 2018 and 2021, the Distinguished Young Scholars of Shandong Province in 2016, the Guan Zhaozhi Award in 2012, and the Best Student Paper Award at the 10th WCICA in 2012.

Xinrong Yang, received the B.S. degree from the School of Mathematics and Statistics, Shandong Normal University, P.R. China in 2019. She is currently pursuing the Ph.D. degree at the School of Mathematics and Statistics, Shandong Normal University. Her research interests include logical dynamic systems, robust control, etc. She won the First Class Prize of Excellent Student's Paper in the

9th TCCT Stochastic System and Control Conference.

Wenrong Li, received the B.S. degree from the School of Mathematics and Statistics, Shandong Normal University, P.R. China in 2022. She is currently pursuing the Ph.D. degree at the School of Mathematics and Statistics, Shandong Normal University. Her research interests include Boolean matrix theory, logical dynamic systems, etc. She won the First Class Prize of Excellent Student’s Paper in the 10th TCCT Stochastic System and Control Conference.