Location
M3 3103
Candidate
Ivan Shevchenko | Applied Math, University of Waterloo
Title
Stability Analysis of Switched Dynamical Systems
Abstract
In many applications, dynamical systems may display abrupt changes between different modes of operation; examples are plentiful in the studies of power systems, traffic control, epidemiology, robotics, and numerous other topics in various scientific and engineering disciplines. Such phenomena are often best modelled as switched systems, which are given by a collection of "subsystems" defined on the same state space together with a time-dependent "switching signal" specifying which subsystem governs the dynamics at a given moment in time. The subsystems are often assumed to admit a common equilibrium point, and a central question in switched systems theory is to investigate asymptotic stability properties of this equilibrium point.
One approach of addressing this question is to find conditions on the subsystem dynamics such that asymptotic stability holds uniformly over all possible switching signals. In the case of continuous-time and linear subsystem dynamics in two-dimensional state-space, I will present novel necessary and sufficient conditions for such uniform asymptotic stability to hold. A complementary and underdeveloped approach for stability analysis of switched systems involves fixing the subsystem dynamics and characterizing the set of switching signals which result in asymptotic stability. Again assuming continuous-time linear dynamics, I will discuss recently published work in which an approximate characterization of such stabilizing switching signals is given in the time-periodic setting. Additionally, I will talk about a new framework for estimating the domain of attraction under automaton-constrained switching signals in the discrete-time nonlinear setting, effectively extending the classical Zubov's method originally developed for unswitched systems. I will conclude by discussing future research directions pertaining to networks of switched systems.