Dr. Chirayu Athalye, Inspire faculty at EE presents “Comparison Between Different Notions of Stability for Laurent Systems”
Title: Comparison Between Different Notions of Stability for Laurent Systems
Speaker : Dr. Chirayu Athalye
Venue: MMCR, first floor, electrical Engineering department
Date & time : Friday 7th June, 4:00 PM
Abstract: Most of the systems in modern-day engineering applications are governed by either partial differential/difference equations (n-D systems) or delay-differential equations. Such systems can be modeled as infinite dimensional dynamical systems. A crucial question regarding the dynamical systems defined over an infinite dimensional state-space is that of stability. However, as the underlying state-space is infinite dimensional, generalization of results about the stability of finite dimensional systems is not straightforward and can be counter-intuitive.
In this talk, we examine a particular family of infinite dimensional discrete autonomous systems, which are governed by a Laurent polynomial matrix in the shift operator. We call this family of systems as Laurent systems. A Laurent system emerges in many interesting scenarios – namely, time-relevant discrete 2-D systems, the formation problem of infinite chains of agents, repetitive processes encountered in coal-cutting and metal-rolling industries, discrete quantum mechanics, etc. In this talk, we compare four different notions of stability for Laurent systems, and explain how some of the stability results are counter-intuitive when compared with the case of finite dimensional systems.
Bio: Chirayu obtained his M.Tech. and Ph.D. degrees from IIT Bombay. Currently he is an INSPIRE faculty at IISc. His research interests include infinite dimensional systems, n-D systems, stability analysis of dynamical systems, optimal control, and convex optimization.