Spectrum-based Methods and Algorithms for the Robustness Stability Analysis of Delay Systems

The dynamic behavior of a linear time-invariant system is determined by the solutions of an eigenvalue problem. Dynamical systems are often subject to physical parameters with an important level of uncertainty. Application engineers then want to know how sensitive the system is with respect to these parameters, for example, how much a parameter may change without losing stability or a performance level. In this thesis we focus on a worst-case analysis in the uncertainty quantification. This leads us to eigenvalue problems with uncertainty. The question how the performance or robustness of the system can be optimized by a careful choice of design parameters or by active or passive control, leads us to eigenvalue optimization problems. Recently, significant advances have been obtained on robust control design approaches, which are grounded in eigenvalue optimization, as well as on solving nonlinear eigenvalue problems, which arise in the analysis of classes of large-scale systems. The aim of the PhD project is to shift the state-of-the-art from control of stand-alone systems to large networks of interconnected systems. The goal is to compute simple controllers, which are easy to implement, and possibly decentralized, i.e., where a global objective is reached by local actions. The project will be realized by combining advances in numerical linear algebra, control theory, numerical optimization, and approximation theory. The methods and algorithms are validated on problems from mechanical and electrical engineering (traffic flow control, communication networks,…), through ongoing collaborations with applications oriented research groups.

Publication year:2020

Accessibility:Open