Spectrum Asymptotics of Operator Pencils (14rit182)

The Banff International Research Station will host the "Spectrum Asymptotics of Operator Pencils" workshop from to .

The root locus is an important tool for controller design and analysis. It reveals the dependence of the stability and dynamics of a controlled system on a parameter, often the controller gain. However, many systems, such as vibrations and acoustic noise are modelled by partial differential equations or delay equations and the root locus of these systems has not been well-defined. These systems evolve on an infinite-dimensional space and so the root locus has an infinite number of branches. The asymptotic behaviour can be quite different from that for finite-dimensional systems. The behaviour of the root locus can be quite different from that of computer calculations based on approximations and so theoretical analysis is needed.

The problem of defining and analyzing the root locus of infinite-dimensional systems can be formulated as determining the asymptotic spectrum of a class of operator pencils. Unfortunately, these theoretical problems have not been well-studied. We plan to look at the dependence of the spectrum of a class of operator pencils on a parameter and thus obtain insight into the nature of the root locus for an important class of control systems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).