On the Role of Well-posedness in Homotopy Methods for the Stability Analysis of Nonlinear Feedback Systems

Sunday, April 26, 2020 - 11:30am - 12:00pm
Keller 3-180
Randy Freeman (Northwestern University)
We consider the problem of determining the input/output stability of the feedback connection of two systems. Popular approaches to this problem include techniques based on dissipativity, topological graph separation, the factorization of multipliers, and integral quadratic
constraints (IQCs). Some of these approaches assume that the feedback connection is well-posed, namely, that the feedback equations have solutions for all possible exogenous inputs and that the mapping from these inputs to the solutions is causal. In particular, this assumption is prominent in the homotopy methods pioneered by Megretski and Rantzer for stability analysis using IQCs. In this talk we will explore the role of well-posedness in these homotopy methods. In so doing we will demonstrate that what suffices for the homotopy analysis is a property significantly weaker than well-posedness, one which involves a certain lower hemicontinuity of the feedback connection together with a certain weak stability of the individual systems.