Impulsive Systems with Delays

This book systematically presents the most recent progress in stability and control of impulsive systems with delays. Impulsive systems have recently attracted continued high research interests because they provide a natural framework for mathematical modeling of many real-world processes. It focuses not only on impulsive delayed systems, but also impulsive systems with delayed impulses and impulsive systems with event-triggered mechanism, including their Lyapunov stability, finite-time stability and input-to-state stability synthesis. Special attention is paid to the bilateral effects of the delayed impulses, where comprehensive stability properties are discussed in the framework of time-dependent and state-dependent delays. New original work with event-triggered impulsive control and its applications in multi-agent systems and collective dynamics are also provided.

This book will be of use to specialists who are interested in the theory of impulsive differential equations and impulsive control theory, as well as high technology specialists who work in the fields of complex networks and applied mathematics. Also, instructors teaching graduate courses and graduate students will find this book a valuable source of nonlinear system theory.

• Impulsive Systems
• Time Delay
• Existence And Uniqueness Of Solutions
• Observability And Controllability
• Lyapunov Stability
• Input-to-state Stability
• Finite-time Stability
• Synchronization Control
• Delayed Impulses
• Impulsive Control
• Impulsive Disturbance
• Event-triggered Mechanism
• Event-triggered Impulsive Control

• School of Mathematics and Statistics, Shandong Normal University, Jinan, China

  Xiaodi Li

• Department of Automation, Tsinghua University, Beijing, China

  Shiji Song

Xiaodi Li was born in Shandong province, China. He received the B.S. and M.S. degrees from Shandong Normal University, Jinan, China, in 2005 and 2008, respectively, and the Ph.D. degree from Xiamen University, Xiamen, China, in 2011, all in applied mathematics. He joined the School of Mathematics and Statistics, Shandong Normal University, Jinan, China, in 2011. He is currently Professor and Director of the Research Center for Control and Engineering Computation. From May 2019, he is Dean of the School of Mathematics and Statistics, Shandong Normal University. From November 2014 to December 2016, he was Visiting Research Fellow at Laboratory for Industrial and Applied Mathematics in York University, Canada, and the University of Texas at Dallas, USA. From 2017 to 2019, he was Visiting Research Fellow at the Department of Mathematics in City University of Hong Kong and the Department of Mechanical Engineering in The University of Hong Kong, respectively. He is currently Editor-in-Chief of the 'AIMS Mathematics' and 'Mathematical Modelling and Control', Subject Editor of Applied Mathematical Modelling, Associate Editor of International Journal of Systems Science, Neural Processing Letters, etc. He has authored or co-authored more than 100 research papers. His current research interests include discontinuous control theory, delay systems, hybrid systems, artificial neural networks, and applied mathematics.

Shiji Song was born in 1965. He received the B.S. in Mathematics from Harbin Normal University, China, in 1986, and M.S. and Ph.D. degrees in Mathematics from Harbin Institute of Technology, China, in 1989 and 1996, respectively. Since 2000, he has been with the Department of Automation, Tsinghua University, China, where he is currently Professor. His research and teaching interests include system identification, fuzzy systems, stochastic neural network, and visual information system for ocean mineral resource and its application.  He has published in various well-established journals, including IIE Transactions, Journal of Scheduling, European Journal of Operational Research, Journal of the Operational Research Society, IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Circuits and Systems, and many others.

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