Malakorn, Tanit (Naresuan Univ.), Ball, Joseph A. (Virginia Tech.), Groenewald, Gilbert J. (North-West Univ.)

Robust Control for Structured Noncommutative Multidimensional Linear Systems

Scheduled for presentation during the Mini-Symposium "Multidimensional Systems: Noncommutative and Overdetermined Systems I" (FrA05), Friday, July 28, 2006, 11:40−12:05, 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 18, 2024

Abstract

The main purpose of this talk is to obtain a Bounded Real Lemma (with both a standard and strict formulation) for formal power series in noncommuting variables, which can be regarded as the formal transfer functions of structured noncommutative multidimensional linear systems (SNMSs) introduced by the authors. We then prove this Bounded Real Lemma as an application of the state-space similarity theorem for SNMLSs combined with the conservative realization theorem for formal power series assuming contractive values when evaluated on contractive time-varying operator tuples. We also show how this Bounded Real Lemma implies and is easily obtained from recent results on robust control of systems with structured time-varying uncertainties. Finally we show how the linear-fractional model for a 1-D plant with structured time-varying uncertatinty and the characterizations of uniform robust stability and uniform robust performance given there fit conveniently into our structure-graph setting here.