On Duality for Lyapunov Functions of Nonstrict Convex Processes

This paper provides a novel definition for Lyapunov functions for difference inclusions defined by convex processes. It is shown that this definition reflects stability properties of nonstrict convex processes better than previously used definitions. In addition the paper presents conditions under which a weak Lyapunov function for a convex process yields a strong Lyapunov function for the dual of the convex process

Celebrating Faculty Scholarship: Bibliography - 2011

A bibliography of faculty publications submitted for inclusion in the fourth annual \u27Celebrating Faculty Scholarship\u27 event sponsored by Loyola University Libraries. The event, which took place on October 24, 2012 in the Richard J. Klarchek Information Commons on the university\u27s Lake Shore Campus, featured articles, books, creative works, and other materials authored by Loyola University Chicago faculty in 2011

A geometric framework for constraints and data:from linear systems to convex processes

In part one of this thesis we develop the theory of analyis of convex processes. The results of this development can be directly applied to the analysis of discrete time, linear, time-invariant mathematical systems with conic constraints. Such constraints arise from physical properties of natural phenomena, and hence it is important that these are considered in the mathematical models thereof. In part two we focus determining whether a system has a given system theoretic property on the basis of measured data. For this, we develop the informativity framework, which allows us to consider and resolve a large number of such problems