## Department Colloquium

### Friday, November 30th, 2018

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Kexue Zhang (Queen's University)

**Title:** Input-to-State Stability of Impulsive Systems with Time-Delay

**Abstract: ** Impulsive systems are dynamical systems subject to state jumps at a sequence of discrete-time moments. These systems are often modelled by impulsive differential equations, and have applications in a wide variety of areas, including network synchronization and epidemic dynamics. Time-delay is an essential part of most practical scenarios of impulsive systems. For instance, time-delay is unavoidable in sampling and transmission of the impulse information. In this talk, I will given an overview of the fundamental theory of impulsive functional differential equations, which provide the mathematical building blocks for studying impulsive time-delay systems. I then discuss the stability of the evolution of these systems, where I will focus on the input-to-state stability problem. As an application, impulsive synchronization of time-delay systems will be studied. This is joint work with Xinzhi Liu (Waterloo).

**Kexue Zhang** obtained his Ph.D. degree in the Department of Applied Mathematics, University of Waterloo,Canada in 2017. He is currently a Coleman Postdoctoral Fellow at Queen's University. His research interests include hybrid systems and control, differential equations on time scales, and their various applications on complex dynamical networks.