PhD Defense: "Towards a Robust Stability Theory for Stochastic Hybrid Systems"

Anantharaman Subbaraman

December 7th (Monday), 10:00am
Building 406, Room 216

In this work, we focus on developing analysis tools related to stability theory for stochastic systems modeled by set-valued mappings. We begin by developing analysis tools for a simple class of discrete-time stochastic systems and then extend the results to a larger class of stochastic hybrid systems. Stochastic hybrid systems are a class of dynamical systems that combine continuous-time dynamics, discrete-time dynamics and randomness.

The analysis tools are established for stochastic properties like global asymptotic stability in probability and global recurrence. We establish results related to four main types of analysis tools. Firstly, sufficient conditions for certifying stability properties are established using Lyapunov-like functions satisfying strict decrease properties on average along solutions. Secondly, weak sufficient conditions that relax the strict decrease nature of the Lyapunov-like function along solutions are established based on the invariance principle. Thirdly, robust stability conditions that determine when stability properties are robust to sufficiently small perturbations of the nominal system data are studied. Finally, we focus on developing converse Lyapunov theorems that illustrate the equivalence between asymptotic properties of a system and the existence of a function that satisfies a strict decrease condition on average along the solutions.

About Anantharaman Subbaraman:

photo of Anantharaman Subbaraman Anantharaman Subbaraman received his B.Tech. degree in Instrumentation and Control Engineering from the National Institute of Technology, Trichy, India, in 2010. He secured his M.S. degree in Electrical and Computer Engineering (ECE) from the University of California, Santa Barbara (UCSB), in 2011, where he is currently pursuing his Ph.D. degree under the guidance of Prof. Andrew R. Teel. His research interests include stability and control of hybrid systems and stochastic hybrid systems.

Hosted by: Professor Andrew R.Teel