Ball, Joseph A. (Virginia Tech.)

Formal Power Series in Noncommuting Indeterminants: System-Theory Interpretation and Applications

Scheduled for presentation during the Mini-Symposium "Multidimensional Systems: Noncommutative and Overdetermined Systems I" (FrA05), Friday, July 28, 2006, 10:25−11:15, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

Formal power series in noncommuting indeterminants were studied several decades ago in connection with the theory of formal languages and finite automata as well as with the state-space realization theory for various types of nonlinear input-output systems. More recently they have been used in the analysis of robust control for input-state-output linear systems having a linear-fractional-modelled structured time-varying uncertainty, in the realization theory of switched linear systems, and in the quest for a systematic procedure for the reduction of general rational matrix inequalities to Linear Matrix Inequalities. In a more conceptual vein, recent work has identified formal power series in noncommuting indeterminants as the analogue of the transfer function for a noncommutative linear system (a multidimensional linear system with evolution along a free semigroup rather than along an integer lattice). This talk will survey and connect these various occurrences of formal power series in noncommuting indeterminants from the point of system theory. This is an update of a similar lecture given at the NDS 2005 meeting in Wuppertal, Germany in July 2005.