Theory of Hybrid Systems: Deterministic and Stochastic

Dr. Mohamad S. Alwan is a lecturer at the Department of Applied Mathematics at the University of Waterloo. Since 2004, his research interests have been directed towards broadening the research area of “Stochastic and Deterministic Hybrid Systems with/without Time Delay and Applications to Control Systems”. Specifically, he has been working on establishing many system properties and applying some of these properties to control systems. He has published several peer-reviewed journal papers, conference papers, and book chapters, most of which are included in the book. Professor Xinzhi Liu is a faculty member of the Department of Applied Mathematics at the University of Waterloo. He received his Ph.D. degree in Applied Mathematics from the University of Texas at Arlington. He is an expert on hybrid dynamical systems, stability theory and control methods. He has been the editor-in- chief of the Journal--Dynamics of Continuous, Discrete and Impulsive Systems since 1995. He has published over 300 research papers and 3 monographs and 20 edited books on different topics in the field of dynamical systems.  

Introduction.- Analysis of Hybrid Systems.- Singularly Perturbed Systems (SPSs).- Systems of Dierential Equations with Piecewise Continuous Arguments (EPCA): A Hybrid System Approach.- Reliable Control and State Estimation for Uncertain Impulsive Large-Scale Systems.- Stochastic Hybrid (Impulsive) Systems.- Stochastic Systems with EPCA.- Input-to-State Stability (ISS) for Stochastic Hybrid Systems.- Stability in Terms of Two Measures.